Metrics for Henrywood and Agarwal, Equation (9a)

analyze481.0ms (7.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.7%	0.3%	0%	0%	0%	0
0%	0%	99.7%	0.3%	0%	0%	0%	1
0%	0%	99.7%	0.3%	0%	0%	0%	2
0%	0%	99.7%	0.3%	0%	0%	0%	3
0%	0%	99.7%	0.3%	0%	0%	0%	4
0%	0%	99.7%	0.3%	0%	0%	0%	5
0%	0%	99.7%	0.3%	0%	0%	0%	6
12.5%	12.5%	87.2%	0.3%	0%	0%	0%	7
12.5%	12.5%	87.2%	0.3%	0%	0%	0%	8
12.5%	12.5%	87.2%	0.3%	0%	0%	0%	9
12.5%	12.5%	87.2%	0.3%	0%	0%	0%	10
12.5%	12.5%	87.2%	0.3%	0%	0%	0%	11
18.8%	18.7%	81%	0.3%	0%	0%	0%	12

Compiler

Compiled 25 to 19 computations (24% saved)

Precisions

Click to see histograms. Total time spent on operations: 230.0ms

Operation ival-mult, time spent: 98.0ms, 43.0% of total-time

Operation ival-sqrt, time spent: 39.0ms, 17.0% of total-time

Operation ival-div, time spent: 34.0ms, 15.0% of total-time

Operation ival-pow, time spent: 33.0ms, 14.0% of total-time

Operation ival-sub, time spent: 18.0ms, 8.0% of total-time

Operation const, time spent: 8.0ms, 3.0% of total-time

sample2.3s (37.4%)

Results

1.4s	7098×	valid
480.0ms	2707×	invalid
229.0ms	1157×	infinite
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

Operation ival-mult, time spent: 335.0ms, 32.0% of total-time

Operation ival-sub, time spent: 206.0ms, 20.0% of total-time

Operation ival-div, time spent: 187.0ms, 18.0% of total-time

Operation ival-sqrt, time spent: 151.0ms, 14.0% of total-time

Operation ival-pow, time spent: 123.0ms, 12.0% of total-time

Operation const, time spent: 42.0ms, 4.0% of total-time

Bogosity

preprocess1.6s (26.3%)

Algorithm

1×	egg-herbie

Rules

990×	`cancel-sign-sub-inv`
892×	`associate-/l*`
772×	`neg-mul-1`
744×	`neg-sub0`
716×	`*-commutative`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`h`
-	-	`(*.f64 2 d)`
-	-	`M`
-	-	`l`
-	-	`(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))`
-	-	`(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))`
-	-	`(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))`
-	-	`(pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)`
-	-	`(/.f64 (.f64 M D) (.f64 2 d))`
-	-	`w0`
-	-	`(-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))`
-	-	`(*.f64 M D)`
-	-	`d`
-	-	`2`
-	-	`(/.f64 h l)`
-	-	`D`
-	-	`1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2099
1	567	2083
2	1678	2067
3	5360	2067

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 (neg.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 (neg.f64 M) D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M (neg.f64 D)) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (neg.f64 h) l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h (neg.f64 l))))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 (neg.f64 d))) 2) (/.f64 h l)))))
(neg.f64 (.f64 (neg.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 (neg.f64 M) D) (.f64 2 d)) 2) (/.f64 h l))))))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M (neg.f64 D)) (.f64 2 d)) 2) (/.f64 h l))))))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (neg.f64 h) l))))))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h (neg.f64 l)))))))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 (neg.f64 d))) 2) (/.f64 h l))))))
(.f64 M (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 w0 D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M w0) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 w0 l)))))
(.f64 l (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h w0)))))
(.f64 d (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 w0)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 h D) (.f64 2 d)) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 l D) (.f64 2 d)) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 d D) (.f64 2 M)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M h) (.f64 2 d)) 2) (/.f64 D l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M l) (.f64 2 d)) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M d) (.f64 2 D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 h)) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 l)) 2) (/.f64 h d)))))

Outputs
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 (neg.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))) (neg.f64 w0))
(.f64 w0 (neg.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l))))))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 (neg.f64 M) D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M (neg.f64 D)) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (neg.f64 h) l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 (neg.f64 h) l)))))
(.f64 w0 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l) 1)))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 h l) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h (neg.f64 l))))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 (neg.f64 h) l)))))
(.f64 w0 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l) 1)))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 h l) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 (neg.f64 d))) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(neg.f64 (.f64 (neg.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 (neg.f64 M) D) (.f64 2 d)) 2) (/.f64 h l))))))
(.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))) (neg.f64 w0))
(.f64 w0 (neg.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l))))))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M (neg.f64 D)) (.f64 2 d)) 2) (/.f64 h l))))))
(.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))) (neg.f64 w0))
(.f64 w0 (neg.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l))))))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (neg.f64 h) l))))))
(.f64 (neg.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 (neg.f64 h) l)))))
(.f64 (neg.f64 w0) (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l) 1)))
(.f64 w0 (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 h l) 1))))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h (neg.f64 l)))))))
(.f64 (neg.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 (neg.f64 h) l)))))
(.f64 (neg.f64 w0) (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l) 1)))
(.f64 w0 (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 h l) 1))))
(neg.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 (neg.f64 d))) 2) (/.f64 h l))))))
(.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))) (neg.f64 w0))
(.f64 w0 (neg.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l))))))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 (neg.f64 w0) (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 M (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 w0 D) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 M (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 w0 2) (/.f64 D d)) 2)))))
(.f64 M (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 D d) (/.f64 w0 2)) 2)))))
(.f64 M (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 D (/.f64 (/.f64 w0 2) d)) 2)))))
(.f64 M (sqrt.f64 (neg.f64 (fma.f64 (/.f64 h l) (pow.f64 (.f64 (/.f64 D d) (/.f64 w0 2)) 2) -1))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M w0) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) w0)) 2)))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 w0 2) (/.f64 M d)) 2)))))
(.f64 D (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 M 2) (/.f64 w0 d)) 2)))))
(.f64 D (sqrt.f64 (neg.f64 (fma.f64 (/.f64 h l) (pow.f64 (.f64 w0 (/.f64 (/.f64 M 2) d)) 2) -1))))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 w0 l)))))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 w0 l)))))
(.f64 h (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 w0 l)))))
(.f64 h (sqrt.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 w0 l) -1))))
(.f64 l (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h w0)))))
(.f64 l (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h w0)))))
(.f64 l (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h w0)))))
(.f64 l (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) w0) 1)))
(.f64 l (sqrt.f64 (neg.f64 (fma.f64 h (/.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) w0) -1))))
(.f64 d (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 w0)) 2) (/.f64 h l)))))
(.f64 d (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D w0)) 2)))))
(.f64 d (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M w0)) 2)))))
(.f64 d (sqrt.f64 (neg.f64 (fma.f64 (/.f64 h l) (pow.f64 (.f64 D (/.f64 M (*.f64 w0 2))) 2) -1))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (fma.f64 (pow.f64 (.f64 (/.f64 D (*.f64 d -2)) M) 2) (/.f64 (neg.f64 h) l) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 h D) (.f64 2 d)) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 h (/.f64 (*.f64 2 d) D)) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 h (.f64 2 d)) D) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 h (.f64 2 d))) 2) (/.f64 M l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 l D) (.f64 2 d)) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 l 2) (/.f64 D d)) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 l (.f64 2 d)) D) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 l (/.f64 d (/.f64 D 2))) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 l d) (/.f64 D 2)) 2) (/.f64 h M)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 d D) (.f64 2 M)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 D d) (.f64 M 2)) 2)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 d (/.f64 (*.f64 M 2) D)) 2)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 D 2) (/.f64 d M)) 2)))))
(.f64 w0 (sqrt.f64 (fma.f64 (/.f64 (neg.f64 h) l) (pow.f64 (.f64 (/.f64 D 2) (/.f64 d M)) 2) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M h) (.f64 2 d)) 2) (/.f64 D l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 h d) (/.f64 M 2)) 2) (/.f64 D l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (/.f64 h (/.f64 d M)) 2) 2) (/.f64 D l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M l) (.f64 2 d)) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 l d)) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 (/.f64 M 2) l) d) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 l (/.f64 M (.f64 2 d))) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 l (/.f64 (/.f64 M 2) d)) 2) (/.f64 h D)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M d) (.f64 2 D)) 2) (/.f64 h l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (*.f64 (/.f64 M 2) (/.f64 d D)) 2)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (.f64 d (/.f64 M (.f64 D 2))) 2)))))
(.f64 w0 (sqrt.f64 (fma.f64 (/.f64 h l) (neg.f64 (pow.f64 (.f64 d (/.f64 M (*.f64 D 2))) 2)) 1)))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 D (.f64 d -2)) M) 2) (/.f64 l h)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 h)) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D h)) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 h))) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 D (/.f64 (/.f64 M 2) h)) 2) (/.f64 d l)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 l)) 2) (/.f64 h d)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D l)) 2) (/.f64 h d)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M l) (/.f64 D 2)) 2) (/.f64 h d)))))
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (/.f64 M (.f64 2 l))) 2) (/.f64 h d)))))

Symmetry

(abs M)

(abs D)

(abs d)

(negabs w0)

(sort M D)

Compiler

Compiled 228 to 126 computations (44.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.1s

Operation ival-mult, time spent: 338.0ms, 31.0% of total-time

Operation ival-div, time spent: 273.0ms, 25.0% of total-time

Operation ival-sub, time spent: 185.0ms, 17.0% of total-time

Operation ival-pow, time spent: 135.0ms, 13.0% of total-time

Operation ival-sqrt, time spent: 97.0ms, 9.0% of total-time

Operation const, time spent: 48.0ms, 4.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 78 to 50 computations (35.9% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	82.1%	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
▶	82.3%	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))

Compiler

Compiled 48 to 36 computations (25% saved)

localize1.5s (24.3%)

Compiler: Compiled 199 to 108 computations (45.7% saved)
Precisions: Click to see histograms. Total time spent on operations: 1.1s
Operation ival-div, time spent: 349.0ms, 31.0% of total-time
Operation ival-mult, time spent: 304.0ms, 27.0% of total-time
Operation ival-sub, time spent: 187.0ms, 17.0% of total-time
Operation ival-pow, time spent: 138.0ms, 12.0% of total-time
Operation ival-sqrt, time spent: 96.0ms, 9.0% of total-time
Operation const, time spent: 47.0ms, 4.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 6 to 6 computations (0% saved)

prune3.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	0	0
Total	2	2

Accuracy

82.9%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	82.1%	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
✓	82.3%	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))

Compiler

Compiled 108 to 76 computations (29.6% saved)

regimes56.0ms (0.9%)

Accuracy

Total -1.0b remaining (-8.6%)

Threshold costs -1b (-8.6%)

Counts

3 → 1

Calls

Call 1

Inputs

(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))

(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))

(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))

Outputs
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))

Calls

15 calls:

9.0ms	w0
6.0ms	(-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))
4.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0ms	(*.f64 2 d)
3.0ms	h

Results

Accuracy	Segments	Branch
82.3%	1	`w0`
82.3%	1	`M`
82.3%	1	`D`
82.3%	1	`h`
82.3%	1	`l`
82.3%	1	`d`
82.3%	1	`(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))`
82.3%	1	`(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))`
82.3%	1	`(-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))`
82.3%	1	`(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))`
82.3%	1	`(pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)`
82.3%	1	`(/.f64 (.f64 M D) (.f64 2 d))`
82.3%	1	`(*.f64 M D)`
82.3%	1	`(*.f64 2 d)`
82.3%	1	`(/.f64 h l)`

Compiler

Compiled 183 to 145 computations (20.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative`
10×	`sub-neg`
10×	`+-commutative`
8×	`neg-mul-1`
8×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	71
1	40	71
2	51	71
3	59	71
4	65	71
5	68	71
6	69	71

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))

Outputs
(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 D 2) (/.f64 M d)) 2) (/.f64 h l)))))

Compiler

Compiled 24 to 18 computations (25% saved)

soundness111.0ms (1.8%)

Rules

990×	`cancel-sign-sub-inv`
892×	`associate-/l*`
772×	`neg-mul-1`
744×	`neg-sub0`
716×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2099
1	567	2083
2	1678	2067
3	5360	2067

Stop Event

1×	node limit

end0.0ms (0%)

preprocess71.0ms (1.2%)

Remove

(negabs w0)

(abs d)

Compiler

Compiled 864 to 648 computations (25% saved)

analyze481.0ms (7.9%)

sample2.3s (37.4%)

preprocess1.6s (26.3%)

eval1.0ms (0%)

prune2.0ms (0%)

localize1.5s (24.3%)

eval0.0ms (0%)

prune3.0ms (0%)

regimes56.0ms (0.9%)

simplify4.0ms (0.1%)

soundness111.0ms (1.8%)

end0.0ms (0%)

preprocess71.0ms (1.2%)

Profiling