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

start0.0ms (0%)

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

analyze425.0ms (5.1%)

Memory

-27.8MiB live, 777.7MiB allocated; 161ms collecting garbage

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
0%	0%	99.8%	0.2%	0%	0%	0%	5
0%	0%	99.8%	0.2%	0%	0%	0%	6
0%	0%	99.8%	0.2%	0%	0%	0%	7
0%	0%	99.8%	0.2%	0%	0%	0%	8
4.2%	3.1%	71.7%	0.2%	0%	25%	0%	9
4.2%	3.1%	71.3%	0.2%	0%	25.3%	0%	10
6.3%	4.7%	69.2%	0.2%	0%	25.9%	0%	11
9.2%	6.6%	65.8%	0.2%	0%	27.4%	0%	12

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample7.1s (86.1%)

Memory

-128.8MiB live, 4 983.7MiB allocated; 5.1s collecting garbage

Samples

1.7s	15 965×	0	invalid
853.0ms	8 256×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-mult!: 752.0ms (49.2% of total)

ival-div!: 352.0ms (23% of total)

ival-sqrt: 241.0ms (15.8% of total)

ival-acos: 178.0ms (11.7% of total)

adjust: 5.0ms (0.3% of total)

Bogosity

explain187.0ms (2.3%)

Memory

6.2MiB live, 300.6MiB allocated; 22ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
28	-	1	(3.0787010028705016e-234 -1.7100356174607904e+77 -1.178862561922431e-12 1.8730935827291935e+65)	`(/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))`
10	-	0	-	`(.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t))`
1	-	0	-	`(/.f64 x (*.f64 y #s(literal 27 binary64)))`
0	-	0	-	`t`
0	-	0	-	`#s(literal 3 binary64)`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64))))`
0	-	0	-	`(*.f64 y #s(literal 27 binary64))`
0	-	0	-	`y`
0	-	0	-	`#s(literal 27 binary64)`
0	-	0	-	`z`
0	-	0	-	`(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))`
0	-	0	-	`(acos.f64 (.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t)))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 z #s(literal 2 binary64))`
0	-	0	-	`(sqrt.f64 t)`
0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))`	u/n	24	0
↳	`(/.f64 x (*.f64 y #s(literal 27 binary64)))`	underflow	66
↳	`(.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64))))`	underflow	66
`*.f64`	`(.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t))`	*nu**	10	0
`/.f64`	`(/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))`	o/n	3	0
↳	`(*.f64 y #s(literal 27 binary64))`	overflow	3
↳	`(/.f64 x (*.f64 y #s(literal 27 binary64)))`	overflow	3
↳	`(.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64))))`	overflow	3
`/.f64`	`(/.f64 x (*.f64 y #s(literal 27 binary64)))`	n/o	1	0
↳	`(*.f64 y #s(literal 27 binary64))`	overflow	3

Confusion

	Predicted +	Predicted -
+	3	0
-	35	218

Precision

0.07894736842105263

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	35	0	218

Precision?

0.07894736842105263

Recall?

1.0

Freqs

test

number	freq
0	218
1	38

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

52.0ms

512×

valid

Compiler

Compiled 203 to 58 computations (71.4% saved)

Precisions

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

ival-mult!: 11.0ms (43.8% of total)

ival-acos: 5.0ms (19.9% of total)

ival-div!: 5.0ms (19.9% of total)

ival-sqrt: 4.0ms (15.9% of total)

adjust: 0.0ms (0% of total)

preprocess311.0ms (3.8%)

Memory

-14.6MiB live, 216.2MiB allocated; 61ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	263
1	287	227
2	1042	197
3	3987	197
4	7017	197
0	18	17
0	29	17
1	50	15
2	137	13
3	494	13
4	2142	13
5	5176	13
0	8214	13

Stop Event

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

Calls

Call 1

Inputs

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))

Outputs

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))

(*.f64 (acos.f64 (*.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (sqrt.f64 t) z)) (/.f64 x y))) #s(literal 1/3 binary64))

Symmetry

(sort y z)

Compiler

Compiled 19 to 18 computations (5.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.1%	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))

Status

Accuracy

Program

▶

98.1%

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))

Compiler

Compiled 19 to 18 computations (5.3% saved)

series40.0ms (0.5%)

Memory

14.4MiB live, 59.3MiB allocated; 7ms collecting garbage

Counts

18 → 17

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 3 binary64)
(acos.f64 (.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t)))
(.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t))
(/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))
(.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64))))
(/.f64 x (*.f64 y #s(literal 27 binary64)))
x
(*.f64 y #s(literal 27 binary64))
y
#s(literal 27 binary64)
(*.f64 z #s(literal 2 binary64))
z
#s(literal 2 binary64)
(sqrt.f64 t)
t

Outputs
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))))
#s(approx (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) #s(hole binary64 (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))))
#s(approx (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) #s(hole binary64 (* 1/18 (* (sqrt t) (/ x (* y z))))))
#s(approx (/ (* 3 (/ x (* y 27))) (* z 2)) #s(hole binary64 (* 1/18 (/ x (* y z)))))
#s(approx (* 3 (/ x (* y 27))) #s(hole binary64 (* 1/9 (/ x y))))
#s(approx (/ x (* y 27)) #s(hole binary64 (* 1/27 (/ x y))))
#s(approx x #s(hole binary64 x))
#s(approx (* y 27) #s(hole binary64 (* 27 y)))
#s(approx y #s(hole binary64 y))
#s(approx (* z 2) #s(hole binary64 (* 2 z)))
#s(approx z #s(hole binary64 z))
#s(approx (sqrt t) #s(hole binary64 (sqrt t)))
#s(approx t #s(hole binary64 t))
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))))
#s(approx (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) #s(hole binary64 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))))
#s(approx (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) #s(hole binary64 (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
#s(approx (sqrt t) #s(hole binary64 (* -1 (* (sqrt t) (pow (sqrt -1) 2)))))

Calls

12 calls:

Time	Variable		Point	Expression
9.0ms	y	@	inf	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (/ 1 3) 1 3 (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) (/ (* 3 (/ x (* y 27))) (* z 2)) (* 3 (/ x (* y 27))) (/ x (* y 27)) x (* y 27) y 27 (* z 2) z 2 (sqrt t) t)
4.0ms	t	@	0	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (/ 1 3) 1 3 (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) (/ (* 3 (/ x (* y 27))) (* z 2)) (* 3 (/ x (* y 27))) (/ x (* y 27)) x (* y 27) y 27 (* z 2) z 2 (sqrt t) t)
4.0ms	y	@	0	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (/ 1 3) 1 3 (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) (/ (* 3 (/ x (* y 27))) (* z 2)) (* 3 (/ x (* y 27))) (/ x (* y 27)) x (* y 27) y 27 (* z 2) z 2 (sqrt t) t)
4.0ms	x	@	inf	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (/ 1 3) 1 3 (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) (/ (* 3 (/ x (* y 27))) (* z 2)) (* 3 (/ x (* y 27))) (/ x (* y 27)) x (* y 27) y 27 (* z 2) z 2 (sqrt t) t)
3.0ms	x	@	0	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (/ 1 3) 1 3 (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) (/ (* 3 (/ x (* y 27))) (* z 2)) (* 3 (/ x (* y 27))) (/ x (* y 27)) x (* y 27) y 27 (* z 2) z 2 (sqrt t) t)

rewrite57.0ms (0.7%)

Memory

-0.5MiB live, 106.3MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	353
0	90	340
0	186	340

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

35 → 51

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(literal 1 binary64)
#s(literal 3 binary64)
(acos.f64 (.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t)))
(.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t))
(/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))
(.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64))))
(/.f64 x (*.f64 y #s(literal 27 binary64)))
x
(*.f64 y #s(literal 27 binary64))
y
#s(literal 27 binary64)
(*.f64 z #s(literal 2 binary64))
z
#s(literal 2 binary64)
(sqrt.f64 t)
t
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))))
#s(approx (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) #s(hole binary64 (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))))
#s(approx (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) #s(hole binary64 (* 1/18 (* (sqrt t) (/ x (* y z))))))
#s(approx (/ (* 3 (/ x (* y 27))) (* z 2)) #s(hole binary64 (* 1/18 (/ x (* y z)))))
#s(approx (* 3 (/ x (* y 27))) #s(hole binary64 (* 1/9 (/ x y))))
#s(approx (/ x (* y 27)) #s(hole binary64 (* 1/27 (/ x y))))
#s(approx x #s(hole binary64 x))
#s(approx (* y 27) #s(hole binary64 (* 27 y)))
#s(approx y #s(hole binary64 y))
#s(approx (* z 2) #s(hole binary64 (* 2 z)))
#s(approx z #s(hole binary64 z))
#s(approx (sqrt t) #s(hole binary64 (sqrt t)))
#s(approx t #s(hole binary64 t))
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))))
#s(approx (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) #s(hole binary64 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))))
#s(approx (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) #s(hole binary64 (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
#s(approx (sqrt t) #s(hole binary64 (* -1 (* (sqrt t) (pow (sqrt -1) 2)))))

Outputs
(.f64 (acos.f64 (.f64 (sqrt.f64 t) (.f64 (/.f64 #s(literal 3 binary64) z) (/.f64 (/.f64 x (.f64 #s(literal 27 binary64) y)) #s(literal 2 binary64))))) #s(literal 1/3 binary64))
(.f64 #s(literal 1/3 binary64) (acos.f64 (.f64 (sqrt.f64 t) (.f64 (/.f64 #s(literal 3 binary64) z) (/.f64 (/.f64 x (.f64 #s(literal 27 binary64) y)) #s(literal 2 binary64))))))
#s(literal 1/3 binary64)
#s(literal 1 binary64)
#s(literal 3 binary64)
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (.f64 (sqrt.f64 t) (.f64 (/.f64 #s(literal 3 binary64) z) (/.f64 (/.f64 x (*.f64 #s(literal 27 binary64) y)) #s(literal 2 binary64))))))
(acos.f64 (.f64 (sqrt.f64 t) (.f64 (/.f64 #s(literal 3 binary64) z) (/.f64 (/.f64 x (*.f64 #s(literal 27 binary64) y)) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 t) (.f64 (/.f64 #s(literal 3 binary64) z) (/.f64 (/.f64 x (*.f64 #s(literal 27 binary64) y)) #s(literal 2 binary64))))
(.f64 (.f64 (/.f64 #s(literal 3 binary64) z) (/.f64 (/.f64 x (*.f64 #s(literal 27 binary64) y)) #s(literal 2 binary64))) (sqrt.f64 t))
(/.f64 (.f64 (.f64 (/.f64 x (.f64 #s(literal 27 binary64) y)) #s(literal 3 binary64)) (sqrt.f64 t)) (.f64 #s(literal 2 binary64) z))
(.f64 (/.f64 #s(literal 3 binary64) z) (/.f64 (/.f64 x (.f64 #s(literal 27 binary64) y)) #s(literal 2 binary64)))
(.f64 #s(literal 3 binary64) (/.f64 (/.f64 x (.f64 #s(literal 27 binary64) y)) (*.f64 #s(literal 2 binary64) z)))
(/.f64 (/.f64 (.f64 (/.f64 x (.f64 #s(literal 27 binary64) y)) #s(literal 3 binary64)) z) #s(literal 2 binary64))
(/.f64 (neg.f64 (.f64 (/.f64 x (.f64 #s(literal 27 binary64) y)) #s(literal 3 binary64))) (neg.f64 (*.f64 #s(literal 2 binary64) z)))
(/.f64 (.f64 (/.f64 x (.f64 #s(literal 27 binary64) y)) #s(literal 3 binary64)) (*.f64 #s(literal 2 binary64) z))
(.f64 (/.f64 x (.f64 #s(literal 27 binary64) y)) #s(literal 3 binary64))
(.f64 #s(literal 3 binary64) (/.f64 x (.f64 #s(literal 27 binary64) y)))
(/.f64 (.f64 #s(literal 3 binary64) x) (.f64 #s(literal 27 binary64) y))
(/.f64 (neg.f64 x) (neg.f64 (*.f64 #s(literal 27 binary64) y)))
(/.f64 (/.f64 x y) #s(literal 27 binary64))
(/.f64 x (*.f64 #s(literal 27 binary64) y))
x
(*.f64 #s(literal 27 binary64) y)
(*.f64 y #s(literal 27 binary64))
y
#s(literal 27 binary64)
(*.f64 #s(literal 2 binary64) z)
(*.f64 z #s(literal 2 binary64))
(+.f64 z z)
z
#s(literal 2 binary64)
(pow.f64 t #s(literal 1/2 binary64))
(sqrt.f64 t)
t
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (.f64 z y)))) #s(literal 1/3 binary64)))
#s(approx (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (*.f64 z y)))))
#s(approx (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (*.f64 z y))))
#s(approx (/ (* 3 (/ x (* y 27))) (* z 2)) (.f64 (/.f64 x (.f64 z y)) #s(literal 1/18 binary64)))
#s(approx (* 3 (/ x (* y 27))) (*.f64 (/.f64 x y) #s(literal 1/9 binary64)))
#s(approx (/ x (* y 27)) (*.f64 #s(literal 1/27 binary64) (/.f64 x y)))
#s(approx x x)
#s(approx (* y 27) (*.f64 #s(literal 27 binary64) y))
#s(approx y y)
#s(approx (* z 2) (*.f64 #s(literal 2 binary64) z))
#s(approx z z)
#s(approx (sqrt t) (sqrt.f64 t))
#s(approx t t)
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (.f64 (/.f64 x y) (/.f64 #s(literal -1 binary64) z)))) #s(literal 1/3 binary64)))
#s(approx (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))) (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (*.f64 (/.f64 x y) (/.f64 #s(literal -1 binary64) z)))))
#s(approx (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)) (.f64 (.f64 #s(literal -1/18 binary64) (sqrt.f64 t)) (*.f64 (/.f64 x y) (/.f64 #s(literal -1 binary64) z))))
#s(approx (sqrt t) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 t))))

eval8.0ms (0.1%)

Memory: -28.8MiB live, 17.9MiB allocated; 2ms collecting garbage
Compiler: Compiled 1 116 to 218 computations (80.5% saved)

prune2.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	1	53

Accuracy

98.5%

Counts

53 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (.f64 z y)))) #s(literal 1/3 binary64)))

Compiler

Compiled 33 to 28 computations (15.2% saved)

series19.0ms (0.2%)

Memory

3.0MiB live, 50.5MiB allocated; 1ms collecting garbage

Counts

14 → 18

Calls

Call 1

Inputs
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (.f64 z y)))) #s(literal 1/3 binary64)))
(.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (.f64 z y)))) #s(literal 1/3 binary64))
(acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (*.f64 z y))))
(.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (*.f64 z y)))
(*.f64 #s(literal 1/18 binary64) (sqrt.f64 t))
#s(literal 1/18 binary64)
(sqrt.f64 t)
t
(/.f64 x (*.f64 z y))
x
(*.f64 z y)
z
y
#s(literal 1/3 binary64)

Outputs
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))))
#s(approx (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))))
#s(approx (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) #s(hole binary64 (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))))
#s(approx (* (* 1/18 (sqrt t)) (/ x (* z y))) #s(hole binary64 (* 1/18 (* (sqrt t) (/ x (* y z))))))
#s(approx (/ x (* z y)) #s(hole binary64 (/ x (* y z))))
#s(approx x #s(hole binary64 x))
#s(approx (* z y) #s(hole binary64 (* y z)))
#s(approx y #s(hole binary64 y))
#s(approx z #s(hole binary64 z))
#s(approx (* 1/18 (sqrt t)) #s(hole binary64 (* 1/18 (sqrt t))))
#s(approx (sqrt t) #s(hole binary64 (sqrt t)))
#s(approx t #s(hole binary64 t))
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))))
#s(approx (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))))
#s(approx (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) #s(hole binary64 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))))
#s(approx (* (* 1/18 (sqrt t)) (/ x (* z y))) #s(hole binary64 (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
#s(approx (* 1/18 (sqrt t)) #s(hole binary64 (* -1/18 (* (sqrt t) (pow (sqrt -1) 2)))))
#s(approx (sqrt t) #s(hole binary64 (* -1 (* (sqrt t) (pow (sqrt -1) 2)))))

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	z	@	inf	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) (* (* 1/18 (sqrt t)) (/ x (* z y))) (* 1/18 (sqrt t)) 1/18 (sqrt t) t (/ x (* z y)) x (* z y) z y 1/3)
2.0ms	t	@	-inf	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) (* (* 1/18 (sqrt t)) (/ x (* z y))) (* 1/18 (sqrt t)) 1/18 (sqrt t) t (/ x (* z y)) x (* z y) z y 1/3)
2.0ms	z	@	-inf	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) (* (* 1/18 (sqrt t)) (/ x (* z y))) (* 1/18 (sqrt t)) 1/18 (sqrt t) t (/ x (* z y)) x (* z y) z y 1/3)
2.0ms	x	@	-inf	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) (* (* 1/18 (sqrt t)) (/ x (* z y))) (* 1/18 (sqrt t)) 1/18 (sqrt t) t (/ x (* z y)) x (* z y) z y 1/3)
2.0ms	y	@	-inf	((* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) (* (* 1/18 (sqrt t)) (/ x (* z y))) (* 1/18 (sqrt t)) 1/18 (sqrt t) t (/ x (* z y)) x (* z y) z y 1/3)

rewrite29.0ms (0.4%)

Memory

-2.1MiB live, 45.2MiB allocated; 1ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	379
0	84	360
0	191	360

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

32 → 44

Calls

Call 1

Inputs
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (.f64 z y)))) #s(literal 1/3 binary64)))
(.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (.f64 z y)))) #s(literal 1/3 binary64))
(acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (*.f64 z y))))
(.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (*.f64 z y)))
(*.f64 #s(literal 1/18 binary64) (sqrt.f64 t))
#s(literal 1/18 binary64)
(sqrt.f64 t)
t
(/.f64 x (*.f64 z y))
x
(*.f64 z y)
z
y
#s(literal 1/3 binary64)
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))))
#s(approx (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))))
#s(approx (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) #s(hole binary64 (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))))
#s(approx (* (* 1/18 (sqrt t)) (/ x (* z y))) #s(hole binary64 (* 1/18 (* (sqrt t) (/ x (* y z))))))
#s(approx (/ x (* z y)) #s(hole binary64 (/ x (* y z))))
#s(approx x #s(hole binary64 x))
#s(approx (* z y) #s(hole binary64 (* y z)))
#s(approx y #s(hole binary64 y))
#s(approx z #s(hole binary64 z))
#s(approx (* 1/18 (sqrt t)) #s(hole binary64 (* 1/18 (sqrt t))))
#s(approx (sqrt t) #s(hole binary64 (sqrt t)))
#s(approx t #s(hole binary64 t))
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))))
#s(approx (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) #s(hole binary64 (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))))
#s(approx (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) #s(hole binary64 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))))
#s(approx (* (* 1/18 (sqrt t)) (/ x (* z y))) #s(hole binary64 (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
#s(approx (* 1/18 (sqrt t)) #s(hole binary64 (* -1/18 (* (sqrt t) (pow (sqrt -1) 2)))))
#s(approx (sqrt t) #s(hole binary64 (* -1 (* (sqrt t) (pow (sqrt -1) 2)))))

Outputs
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (/.f64 x (.f64 z y)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)))) #s(literal 1/3 binary64)))
(.f64 (acos.f64 (.f64 (/.f64 x (.f64 z y)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)))) #s(literal 1/3 binary64))
(.f64 #s(literal 1/3 binary64) (acos.f64 (.f64 (/.f64 x (.f64 z y)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (.f64 (/.f64 x (.f64 z y)) (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)))))
(acos.f64 (.f64 (/.f64 x (.f64 z y)) (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t))))
(.f64 (/.f64 x (.f64 z y)) (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)))
(.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (*.f64 z y)))
(.f64 (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)) #s(literal 1/18 binary64))
(.f64 #s(literal 1/18 binary64) (.f64 (/.f64 x (*.f64 z y)) (sqrt.f64 t)))
(/.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) x) (*.f64 z y))
(*.f64 #s(literal 1/18 binary64) (sqrt.f64 t))
(*.f64 (sqrt.f64 t) #s(literal 1/18 binary64))
#s(literal 1/18 binary64)
(pow.f64 t #s(literal 1/2 binary64))
(sqrt.f64 t)
t
(/.f64 (/.f64 x z) y)
(/.f64 (/.f64 x y) z)
(/.f64 (neg.f64 x) (neg.f64 (*.f64 z y)))
(/.f64 x (*.f64 z y))
x
(*.f64 z y)
(*.f64 y z)
z
y
#s(literal 1/3 binary64)
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (/.f64 x (.f64 z y)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)))) #s(literal 1/3 binary64)))
#s(approx (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) (.f64 (acos.f64 (.f64 (/.f64 x (.f64 z y)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)))) #s(literal 1/3 binary64)))
#s(approx (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) (acos.f64 (.f64 (/.f64 x (.f64 z y)) (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)))))
#s(approx (* (* 1/18 (sqrt t)) (/ x (* z y))) (.f64 (/.f64 x (.f64 z y)) (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t))))
#s(approx (/ x (* z y)) (/.f64 x (*.f64 z y)))
#s(approx x x)
#s(approx (* z y) (*.f64 z y))
#s(approx y y)
#s(approx z z)
#s(approx (* 1/18 (sqrt t)) (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)))
#s(approx (sqrt t) (sqrt.f64 t))
#s(approx t t)
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (.f64 (/.f64 x y) (/.f64 #s(literal -1 binary64) z)))) #s(literal 1/3 binary64)))
#s(approx (* (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) 1/3) (.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (.f64 (/.f64 x y) (/.f64 #s(literal -1 binary64) z)))) #s(literal 1/3 binary64)))
#s(approx (acos (* (* 1/18 (sqrt t)) (/ x (* z y)))) (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (*.f64 (/.f64 x y) (/.f64 #s(literal -1 binary64) z)))))
#s(approx (* (* 1/18 (sqrt t)) (/ x (* z y))) (.f64 (.f64 #s(literal -1/18 binary64) (sqrt.f64 t)) (*.f64 (/.f64 x y) (/.f64 #s(literal -1 binary64) z))))
#s(approx (* 1/18 (sqrt t)) (.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 t)) #s(literal -1/18 binary64)))
#s(approx (sqrt t) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 t))))

eval4.0ms (0.1%)

Memory: 11.9MiB live, 11.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 547 to 191 computations (87.7% saved)

prune23.0ms (0.3%)

Memory

5.8MiB live, 54.8MiB allocated; 4ms collecting garbage

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	1	44

Accuracy

98.5%

Counts

44 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.5%	#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (.f64 z y)))) #s(literal 1/3 binary64)))

Compiler

Compiled 85 to 69 computations (18.8% saved)

regimes17.0ms (0.2%)

Memory

6.5MiB live, 54.1MiB allocated; 1ms collecting garbage

Accuracy

Total -0.2b remaining (-25.4%)

Threshold costs -0.2b (-25.4%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (*.f64 (acos.f64 (*.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (*.f64 z y)))) #s(literal 1/3 binary64)))

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))

Outputs
#s(approx (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))) (.f64 (acos.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) (/.f64 x (.f64 z y)))) #s(literal 1/3 binary64)))

Calls

13 calls:

2.0ms	y
1.0ms	t
1.0ms	(*.f64 y #s(literal 27 binary64))
1.0ms	(.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t))
1.0ms	(.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64))))

Results

Accuracy	Segments	Branch
98.5%	1	`(sqrt.f64 t)`
98.5%	1	`(*.f64 z #s(literal 2 binary64))`
98.5%	1	`(*.f64 y #s(literal 27 binary64))`
98.5%	1	`(/.f64 x (*.f64 y #s(literal 27 binary64)))`
98.5%	1	`(.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64))))`
98.5%	1	`(/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))`
98.5%	1	`(.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t))`
98.5%	1	`(acos.f64 (.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (.f64 z #s(literal 2 binary64))) (sqrt.f64 t)))`
98.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (.f64 (/.f64 (.f64 #s(literal 3 binary64) (/.f64 x (.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))`
98.5%	1	`x`
98.5%	1	`y`
98.5%	1	`z`
98.5%	1	`t`

Compiler

Compiled 83 to 108 computations (-30.1% saved)

derivations4.0ms (0.1%)

Memory

-41.6MiB live, 5.9MiB allocated; 1ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 33 to 28 computations (15.2% saved)

preprocess23.0ms (0.3%)

Memory: 9.7MiB live, 56.7MiB allocated; 2ms collecting garbage
Remove: (sort y z)
Compiler: Compiled 204 to 180 computations (11.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze425.0ms (5.1%)

sample7.1s (86.1%)

explain187.0ms (2.3%)

preprocess311.0ms (3.8%)

eval0.0ms (0%)

prune1.0ms (0%)

series40.0ms (0.5%)

rewrite57.0ms (0.7%)

eval8.0ms (0.1%)

prune2.0ms (0%)

series19.0ms (0.2%)

rewrite29.0ms (0.4%)

eval4.0ms (0.1%)

prune23.0ms (0.3%)

regimes17.0ms (0.2%)

derivations4.0ms (0.1%)

preprocess23.0ms (0.3%)

end0.0ms (0%)

Profiling