Metrics for Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB 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 11 to 11 computations (0% saved)

sample1.3s (36.6%)

Memory

8.4MiB live, 1 299.9MiB allocated; 283ms collecting garbage

Samples

792.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 365.0ms

ival-div: 212.0ms (58% of total)

ival-mult: 69.0ms (18.9% of total)

ival-sub: 64.0ms (17.5% of total)

exact: 8.0ms (2.2% of total)

ival-true: 6.0ms (1.6% of total)

ival-assert: 4.0ms (1.1% of total)

adjust: 2.0ms (0.5% of total)

Bogosity

explain137.0ms (3.7%)

Memory

-18.2MiB live, 142.6MiB allocated; 26ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 8 binary64)`
-	-	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
-	-	`z`
-	-	`(*.f64 x y)`
-	-	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
-	-	`(/.f64 z #s(literal 8 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`y`
-	-	`x`

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

40.0ms

512×

valid

Compiler

Compiled 63 to 31 computations (50.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-div: 7.0ms (49.9% of total)

ival-mult: 4.0ms (28.5% of total)

ival-sub: 2.0ms (14.3% of total)

exact: 1.0ms (7.1% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess16.0ms (0.4%)

Memory

19.6MiB live, 19.6MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	90
1	52	88
2	70	84
3	80	84
4	81	84
0	9	9
0	13	9
1	18	9
2	23	9
3	24	9
0	24	9

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Outputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(-.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Symmetry

(sort x y)

Compiler

Compiled 9 to 9 computations (0% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Compiler

Compiled 9 to 9 computations (0% saved)

simplify4.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 z #s(literal 8 binary64))
cost-diff	0	(*.f64 x y)
cost-diff	0	(/.f64 (*.f64 x y) #s(literal 2 binary64))
cost-diff	0	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
0	13	25
1	18	25
2	23	25
3	24	25
0	24	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(*.f64 x y)
x
y
#s(literal 2 binary64)
(/.f64 z #s(literal 8 binary64))
z
#s(literal 8 binary64)

Outputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(-.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(/.f64 (*.f64 y x) #s(literal 2 binary64))
(*.f64 x y)
(*.f64 y x)
x
y
#s(literal 2 binary64)
(/.f64 z #s(literal 8 binary64))
z
#s(literal 8 binary64)

localize27.0ms (0.7%)

Memory

-6.5MiB live, 39.4MiB allocated; 6ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 (*.f64 x y) #s(literal 2 binary64))
accuracy	0.0	(/.f64 z #s(literal 8 binary64))
accuracy	0.0	(*.f64 x y)
accuracy	0.0078125	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Samples

21.0ms

256×

valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

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

ival-div: 3.0ms (42.5% of total)

ival-mult: 2.0ms (28.4% of total)

ival-sub: 1.0ms (14.2% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

12.7MiB live, 12.7MiB allocated; 0ms collecting garbage

Counts

4 → 12

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(*.f64 x y)
(/.f64 z #s(literal 8 binary64))

Outputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x y)
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) (/ z 8))
1.0ms	x	@	-inf	((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) (/ z 8))
1.0ms	x	@	0	((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) (/ z 8))
1.0ms	y	@	-inf	((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) (/ z 8))
1.0ms	z	@	inf	((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) (/ z 8))

simplify214.0ms (5.8%)

Memory

3.5MiB live, 188.5MiB allocated; 23ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	86
1	128	86
2	433	86
3	1165	86
4	3282	86
5	6444	86
0	8044	78

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 12

Calls

Call 1

Inputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x y)
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))

Outputs
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(* 1/2 (* x y))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
(* x y)
(*.f64 y x)
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))

rewrite162.0ms (4.4%)

Memory

-13.3MiB live, 218.0MiB allocated; 37ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
0	13	20
1	45	20
2	301	20
3	4767	20
0	8947	20

Stop Event

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

Counts

4 → 112

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(*.f64 x y)
(/.f64 z #s(literal 8 binary64))

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64))) (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64)))) (fma.f64 (/.f64 z #s(literal 8 binary64)) (-.f64 (/.f64 z #s(literal 8 binary64)) (/.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64))) (fma.f64 (neg.f64 x) (.f64 y #s(literal -8 binary64)) (.f64 (neg.f64 z) #s(literal -2 binary64)))) #s(literal 16 binary64))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64))) (fma.f64 (neg.f64 x) (.f64 #s(literal 8 binary64) y) (.f64 #s(literal -2 binary64) z))) #s(literal -16 binary64))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64))) (fma.f64 #s(literal -8 binary64) (.f64 y x) (.f64 (neg.f64 z) #s(literal 2 binary64)))) #s(literal -16 binary64))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64))) (fma.f64 #s(literal 8 binary64) (.f64 y x) (.f64 z #s(literal 2 binary64)))) #s(literal 16 binary64))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64))) (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)))) (-.f64 (.f64 (.f64 y x) #s(literal 1/2 binary64)) (.f64 z #s(literal 1/8 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64))) (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal -2 binary64)) #s(literal 4 binary64)) (pow.f64 (/.f64 (.f64 z (fma.f64 #s(literal 8 binary64) (.f64 y x) (.f64 z #s(literal 2 binary64)))) #s(literal 128 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (.f64 z (fma.f64 #s(literal 8 binary64) (.f64 y x) (.f64 z #s(literal 2 binary64)))) #s(literal 128 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64))) (+.f64 (/.f64 (pow.f64 (.f64 z (fma.f64 #s(literal 8 binary64) (.f64 y x) (.f64 z #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 2097152 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal -2 binary64)) #s(literal 6 binary64)))) (fma.f64 (/.f64 (.f64 z (fma.f64 #s(literal 8 binary64) (.f64 y x) (.f64 z #s(literal 2 binary64)))) #s(literal 128 binary64)) (-.f64 (/.f64 (.f64 z (fma.f64 #s(literal 8 binary64) (.f64 y x) (.f64 z #s(literal 2 binary64)))) #s(literal 128 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (/.f64 (.f64 y x) #s(literal -2 binary64)) #s(literal 4 binary64))))
(.f64 (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64))) (/.f64 (-.f64 (.f64 (.f64 y x) #s(literal 1/2 binary64)) (.f64 z #s(literal 1/8 binary64))) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64)))))
(.f64 (fma.f64 (/.f64 (.f64 y z) #s(literal 16 binary64)) x (fma.f64 z (/.f64 z #s(literal 64 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (-.f64 (.f64 (.f64 y x) #s(literal 1/2 binary64)) (.f64 z #s(literal 1/8 binary64))) (fma.f64 (/.f64 (.f64 y z) #s(literal 16 binary64)) x (fma.f64 z (/.f64 z #s(literal 64 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64)))) (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (.f64 y z) #s(literal 16 binary64)) x (fma.f64 z (/.f64 z #s(literal 64 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (.f64 y z) #s(literal 16 binary64)) x (fma.f64 z (/.f64 z #s(literal 64 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (.f64 y z) #s(literal 16 binary64)) x (fma.f64 z (/.f64 z #s(literal 64 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))))) (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (.f64 y z) #s(literal 16 binary64)) x (fma.f64 z (/.f64 z #s(literal 64 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 z #s(literal 1/8 binary64)) #s(literal 2 binary64))) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64)))) (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 x #s(literal 2 binary64)) y (/.f64 z #s(literal 8 binary64))))))))
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(/.f64 (exp.f64 (log.f64 (*.f64 (neg.f64 x) y))) (exp.f64 (log.f64 #s(literal -2 binary64))))
(/.f64 (exp.f64 (log.f64 (*.f64 y x))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 x) y) #s(literal -2 binary64))
(/.f64 (*.f64 y x) #s(literal 2 binary64))
(neg.f64 (/.f64 (*.f64 y x) #s(literal -2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (log.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)))))
(*.f64 (neg.f64 (neg.f64 x)) y)
(*.f64 (neg.f64 (neg.f64 y)) x)
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 x))
(*.f64 y (neg.f64 (neg.f64 x)))
(*.f64 y x)
(*.f64 x (neg.f64 (neg.f64 y)))
(*.f64 x y)
(neg.f64 (*.f64 (neg.f64 x) y))
(pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 1 binary64))
(/.f64 (exp.f64 (log.f64 (neg.f64 z))) (exp.f64 (log.f64 #s(literal -8 binary64))))
(/.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 #s(literal 8 binary64))))
(/.f64 (neg.f64 z) #s(literal -8 binary64))
(/.f64 z #s(literal 8 binary64))
(neg.f64 (/.f64 z #s(literal -8 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 z #s(literal 8 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (/.f64 z #s(literal 8 binary64))))
(+.f64 (cosh.f64 (log.f64 (/.f64 z #s(literal 8 binary64)))) (sinh.f64 (log.f64 (/.f64 z #s(literal 8 binary64)))))

eval14.0ms (0.4%)

Memory: 34.6MiB live, 34.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 921 to 432 computations (85.2% saved)

prune5.0ms (0.1%)

Memory

-38.0MiB live, 7.9MiB allocated; 5ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	2	118

Accuracy

100.0%

Counts

118 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
▶	48.9%	#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify9.0ms (0.2%)

Memory

14.5MiB live, 14.5MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 #s(literal -1/8 binary64) z)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
cost-diff	0	#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
cost-diff	0	(*.f64 #s(literal -1/8 binary64) z)
cost-diff	0	#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	55
0	20	55
1	34	55
2	60	55
3	102	55
4	155	55
5	195	55
6	224	55
7	245	55
0	245	55

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal -1/8 binary64) z)
#s(literal -1/8 binary64)
z
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
y
(*.f64 #s(literal -1/8 binary64) z)
#s(literal -1/8 binary64)
z

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal -1/8 binary64) z)
#s(literal -1/8 binary64)
z
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
y
(*.f64 #s(literal -1/8 binary64) z)
#s(literal -1/8 binary64)
z

localize35.0ms (0.9%)

Memory

15.5MiB live, 69.9MiB allocated; 10ms collecting garbage

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.0	(*.f64 #s(literal -1/8 binary64) z)
accuracy	0.0	#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
accuracy	0.0	(*.f64 #s(literal -1/8 binary64) z)
accuracy	32.687486299454264	#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Samples

27.0ms

256×

valid

Compiler

Compiled 45 to 17 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 10.0ms (59.7% of total)

ival-div: 3.0ms (17.9% of total)

ival-sub: 2.0ms (11.9% of total)

ival-add: 1.0ms (6% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series9.0ms (0.3%)

Memory

-34.5MiB live, 11.2MiB allocated; 11ms collecting garbage

Counts

5 → 11

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal -1/8 binary64) z)
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal 1/2 binary64) x)

Outputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 x)
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	z	@	-inf	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x))
1.0ms	x	@	inf	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x))
1.0ms	x	@	-inf	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x))
1.0ms	x	@	0	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x))
0.0ms	z	@	inf	((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x))

simplify253.0ms (6.9%)

Memory

21.1MiB live, 295.6MiB allocated; 64ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	83
1	128	83
2	434	83
3	1166	83
4	3274	83
5	6465	83
0	8065	75

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 11

Calls

Call 1

Inputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 x)
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))

Outputs
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))

rewrite217.0ms (5.9%)

Memory

30.2MiB live, 278.3MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	45
0	20	45
1	73	45
2	513	43
3	7319	43
0	8326	43

Stop Event

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

Counts

5 → 167

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal -1/8 binary64) z)
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal 1/2 binary64) x)

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal -1/8 binary64) z)
(*.f64 z #s(literal -1/8 binary64))
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 #s(literal -1/64 binary64) (.f64 z z))) (+.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)))) (fma.f64 (/.f64 z #s(literal 8 binary64)) (-.f64 (/.f64 z #s(literal 8 binary64)) (/.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 #s(literal -1/64 binary64) (.f64 z z))) (fma.f64 (neg.f64 x) (.f64 y #s(literal -8 binary64)) (.f64 (neg.f64 z) #s(literal -2 binary64)))) #s(literal 16 binary64))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 #s(literal -1/64 binary64) (.f64 z z))) (fma.f64 (neg.f64 x) (.f64 #s(literal 8 binary64) y) (.f64 #s(literal -2 binary64) z))) #s(literal -16 binary64))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 #s(literal -1/64 binary64) (.f64 z z))) (fma.f64 #s(literal -8 binary64) (.f64 y x) (.f64 (neg.f64 z) #s(literal 2 binary64)))) #s(literal -16 binary64))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 #s(literal -1/64 binary64) (.f64 z z))) (fma.f64 #s(literal 8 binary64) (.f64 y x) (.f64 z #s(literal 2 binary64)))) #s(literal 16 binary64))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64))) (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y)) (/.f64 z #s(literal 8 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y)) (/.f64 z #s(literal 8 binary64)))))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y)) (/.f64 z #s(literal 8 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 6 binary64)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y)) (/.f64 z #s(literal 8 binary64))) (-.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y)) (/.f64 z #s(literal 8 binary64))) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 #s(literal -1/64 binary64) (.f64 z z))) (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 #s(literal 1/512 binary64) (pow.f64 z #s(literal 3 binary64))))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 z (fma.f64 #s(literal 1/64 binary64) z (.f64 (.f64 y x) #s(literal -1/16 binary64))))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 #s(literal -1/64 binary64) (.f64 z z))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 #s(literal -1/64 binary64) (.f64 z z)))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal -1/8 binary64) z) #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) #s(literal 4 binary64)) (pow.f64 (.f64 z (-.f64 (.f64 #s(literal 1/64 binary64) z) (.f64 (.f64 y x) #s(literal -1/16 binary64)))) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/8 binary64) z) (fma.f64 #s(literal -1/8 binary64) z (.f64 #s(literal -1/2 binary64) (.f64 y x))))))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal -1/8 binary64) z) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 z (-.f64 (.f64 #s(literal 1/64 binary64) z) (.f64 (.f64 y x) #s(literal -1/16 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) #s(literal 6 binary64)))) (fma.f64 (.f64 z (-.f64 (.f64 #s(literal 1/64 binary64) z) (.f64 (.f64 y x) #s(literal -1/16 binary64)))) (-.f64 (.f64 z (-.f64 (.f64 #s(literal 1/64 binary64) z) (.f64 (.f64 y x) #s(literal -1/16 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 4 binary64))))
(.f64 (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)) (fma.f64 #s(literal 1/8 binary64) z (.f64 (*.f64 #s(literal 1/2 binary64) x) y))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y)) (/.f64 z #s(literal 8 binary64)) (pow.f64 (/.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y)) (/.f64 z #s(literal 8 binary64)) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 z (-.f64 (.f64 #s(literal 1/64 binary64) z) (.f64 (.f64 y x) #s(literal -1/16 binary64))))) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 z (-.f64 (.f64 #s(literal 1/64 binary64) z) (.f64 (*.f64 y x) #s(literal -1/16 binary64)))))))
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(+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 z (-.f64 (.f64 #s(literal 1/64 binary64) z) (.f64 (.f64 y x) #s(literal -1/16 binary64)))))) (/.f64 (pow.f64 (.f64 #s(literal -1/8 binary64) z) #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 z (-.f64 (.f64 #s(literal 1/64 binary64) z) (.f64 (*.f64 y x) #s(literal -1/16 binary64)))))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y))) (/.f64 (neg.f64 (pow.f64 (.f64 #s(literal -1/8 binary64) z) #s(literal 2 binary64))) (fma.f64 #s(literal 1/8 binary64) z (.f64 (*.f64 #s(literal 1/2 binary64) x) y))))
(+.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y)))) (/.f64 (neg.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/8 binary64) z (.f64 (.f64 #s(literal 1/2 binary64) x) y))))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) (*.f64 (neg.f64 z) #s(literal 1/8 binary64)))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) (/.f64 (*.f64 #s(literal -2 binary64) z) #s(literal 16 binary64)))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) (*.f64 #s(literal -1/8 binary64) z))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) x)) y))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 (neg.f64 (neg.f64 y)) (*.f64 #s(literal 1/2 binary64) x)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 (*.f64 #s(literal 1/2 binary64) x) y))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))

eval26.0ms (0.7%)

Memory: -35.9MiB live, 53.5MiB allocated; 8ms collecting garbage
Compiler: Compiled 7 669 to 707 computations (90.8% saved)

prune3.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	172	3	175

Accuracy

100.0%

Counts

175 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))

▶

52.7%

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))

✓

48.9%

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Compiler

Compiled 46 to 40 computations (13% saved)

simplify4.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y x)
cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 y x))
cost-diff	0	#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
0	15	26
1	23	26
2	35	26
3	38	26
0	38	26

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
#s(literal 1/2 binary64)
(*.f64 y x)
y
x

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 (.f64 y x) #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 y x)
y
x

localize26.0ms (0.7%)

Memory

8.3MiB live, 54.5MiB allocated; 3ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y x)
accuracy	0.0	(.f64 #s(literal 1/2 binary64) (.f64 y x))
accuracy	30.28413257579181	#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))

Samples

18.0ms

256×

valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 6.0ms (56.6% of total)

ival-div: 3.0ms (28.3% of total)

ival-sub: 1.0ms (9.4% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Counts

3 → 11

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(*.f64 y x)

Outputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x y)
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) (* y x))
1.0ms	x	@	-inf	((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) (* y x))
0.0ms	x	@	0	((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) (* y x))
0.0ms	x	@	inf	((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) (* y x))
0.0ms	y	@	inf	((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) (* y x))

simplify206.0ms (5.6%)

Memory

-14.1MiB live, 276.0MiB allocated; 37ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	83
1	128	83
2	433	83
3	1164	83
4	3281	83
5	6436	83
0	8036	75

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 11

Calls

Call 1

Inputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x y)
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))

Outputs
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* x y)
(*.f64 y x)
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) x (.f64 #s(literal -1/8 binary64) z))

rewrite187.0ms (5.1%)

Memory

23.5MiB live, 291.9MiB allocated; 62ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
0	15	23
1	51	23
2	314	23
3	4782	23
0	8960	23

Stop Event

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

Counts

3 → 21

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(*.f64 y x)

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 (.f64 #s(literal 1/2 binary64) y) x))
(.f64 (.f64 #s(literal 1/2 binary64) x) y)
(.f64 (.f64 #s(literal 1/2 binary64) y) x)
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(.f64 #s(literal 8 binary64) (/.f64 (.f64 y x) #s(literal 16 binary64)))
(.f64 (.f64 y x) #s(literal 1/2 binary64))
(.f64 y (/.f64 (.f64 #s(literal 8 binary64) x) #s(literal 16 binary64)))
(.f64 y (.f64 #s(literal 1/2 binary64) x))
(.f64 x (/.f64 (.f64 #s(literal 8 binary64) y) #s(literal 16 binary64)))
(.f64 x (.f64 #s(literal 1/2 binary64) y))
(/.f64 (.f64 (neg.f64 x) (.f64 #s(literal 8 binary64) y)) #s(literal -16 binary64))
(/.f64 (.f64 #s(literal 8 binary64) (.f64 y x)) #s(literal 16 binary64))
(*.f64 (neg.f64 (neg.f64 x)) y)
(*.f64 (neg.f64 (neg.f64 y)) x)
(*.f64 (neg.f64 x) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 x))
(*.f64 y (neg.f64 (neg.f64 x)))
(*.f64 y x)
(*.f64 x (neg.f64 (neg.f64 y)))
(*.f64 x y)
(neg.f64 (*.f64 (neg.f64 x) y))

eval3.0ms (0.1%)

Memory: 9.0MiB live, 9.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 411 to 87 computations (78.8% saved)

prune16.0ms (0.4%)

Memory

-44.8MiB live, 9.7MiB allocated; 14ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	25	3	28

Accuracy

100.0%

Counts

28 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))

✓

52.7%

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))

✓

48.9%

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Compiler

Compiled 101 to 65 computations (35.6% saved)

regimes13.0ms (0.3%)

Memory

27.9MiB live, 27.9MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))

Calls

7 calls:

2.0ms	z
2.0ms	(/.f64 z #s(literal 8 binary64))
2.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`(/.f64 z #s(literal 8 binary64))`
100.0%	1	`(*.f64 x y)`
100.0%	1	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
100.0%	1	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`

Compiler

Compiled 23 to 33 computations (-43.5% saved)

regimes11.0ms (0.3%)

Memory

-20.2MiB live, 28.5MiB allocated; 3ms collecting garbage

Counts

2 → 3

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
#s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))

Outputs

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))

Calls

7 calls:

2.0ms	(/.f64 (*.f64 x y) #s(literal 2 binary64))
1.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
1.0ms	(/.f64 z #s(literal 8 binary64))
1.0ms	z
1.0ms	x

Results

Accuracy	Segments	Branch
76.1%	3	`(/.f64 z #s(literal 8 binary64))`
81.4%	3	`(*.f64 x y)`
81.4%	3	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
70.0%	7	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
76.8%	3	`x`
69.7%	3	`y`
76.1%	3	`z`

Compiler

Compiled 23 to 33 computations (-43.5% saved)

regimes8.0ms (0.2%)

Memory

21.7MiB live, 21.7MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Calls

7 calls:

1.0ms	(/.f64 z #s(literal 8 binary64))
1.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
1.0ms	y
1.0ms	x
1.0ms	z

Results

Accuracy	Segments	Branch
48.9%	1	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
48.9%	1	`y`
48.9%	1	`(/.f64 z #s(literal 8 binary64))`
48.9%	1	`z`
48.9%	1	`x`
48.9%	1	`(*.f64 x y)`
48.9%	1	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`

Compiler

Compiled 23 to 33 computations (-43.5% saved)

bsearch1.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.6321348734823716e-12	1.5414815669835799e-10
0.0ms	-0.05875107531459775	-8.499569058497953e-11

Compiler

Compiled 12 to 15 computations (-25% saved)

simplify46.0ms (1.3%)

Memory

-15.3MiB live, 75.3MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	76
1	35	76
2	40	76
3	44	76
4	51	76
5	73	76
6	231	76
7	1896	76
8	3565	76

Stop Event

1×	node limit

Calls

Call 1

Inputs

#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))

(if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal -3602879701896397/72057594037927936 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) (if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))))

#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) y (.f64 #s(literal -1/8 binary64) z)))
(if (<=.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal -3602879701896397/72057594037927936 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x))) (if (<=.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 #s(literal -1/8 binary64) z)) #s(approx (- (/ ( x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x)))))
(if (or (<=.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal -3602879701896397/72057594037927936 binary64)) (not (<=.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 4951760157141521/2475880078570760549798248448 binary64)))) #s(approx (- (/ (* x y) 2) (/ z 8)) (.f64 #s(literal 1/2 binary64) (.f64 y x))) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

derivations611.0ms (16.7%)

Memory

-1.9MiB live, 400.6MiB allocated; 119ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	86
1	128	86
2	433	86
3	1165	86
4	3282	86
5	6444	86
0	8044	78
0	42	83
1	128	83
2	434	83
3	1166	83
4	3274	83
5	6465	83
0	8065	75

Stop Event

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

Compiler

Compiled 76 to 29 computations (61.8% saved)

preprocess53.0ms (1.4%)

Memory: 8.6MiB live, 103.1MiB allocated; 14ms collecting garbage
Remove: (sort x y)
Compiler: Compiled 206 to 106 computations (48.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.3s (36.6%)

explain137.0ms (3.7%)

preprocess16.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize27.0ms (0.7%)

series7.0ms (0.2%)

simplify214.0ms (5.8%)

rewrite162.0ms (4.4%)

eval14.0ms (0.4%)

prune5.0ms (0.1%)

simplify9.0ms (0.2%)

localize35.0ms (0.9%)

series9.0ms (0.3%)

simplify253.0ms (6.9%)

rewrite217.0ms (5.9%)

eval26.0ms (0.7%)

prune3.0ms (0.1%)

simplify4.0ms (0.1%)

localize26.0ms (0.7%)

series4.0ms (0.1%)

simplify206.0ms (5.6%)

rewrite187.0ms (5.1%)

eval3.0ms (0.1%)

prune16.0ms (0.4%)

regimes13.0ms (0.3%)

regimes11.0ms (0.3%)

regimes8.0ms (0.2%)

bsearch1.0ms (0%)

simplify46.0ms (1.3%)

derivations611.0ms (16.7%)

preprocess53.0ms (1.4%)

end0.0ms (0%)

Profiling