Metrics for Henrywood and Agarwal, Equation (12)

analyze1.0s (13.8%)

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
12.5%	12.5%	87.3%	0.2%	0%	0%	0%	4
12.5%	12.5%	87.3%	0.2%	0%	0%	0%	5
12.5%	12.5%	87.3%	0.2%	0%	0%	0%	6
15.4%	12.5%	68.6%	0.2%	0%	18.7%	0%	7
16.7%	12.5%	62.3%	0.2%	0%	24.9%	0%	8
20%	14%	56.1%	0.2%	0%	29.6%	0%	9
20%	14%	56.1%	0.2%	0%	29.6%	0%	10
20%	14%	56.1%	0.2%	0%	29.6%	0%	11
22.9%	14.8%	49.9%	0.2%	0%	35.1%	0%	12

Compiler

Compiled 41 to 23 computations (43.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 812.0ms

ival-pow: 597.0ms (73.6% of total)

ival-mult: 130.0ms (16% of total)

ival-div: 70.0ms (8.6% of total)

ival-sub: 12.0ms (1.5% of total)

const: 3.0ms (0.4% of total)

sample5.8s (78.1%)

Results

2.6s	13136×	256	invalid
2.1s	8256×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 3.5s

ival-pow: 1.4s (39.7% of total)

ival-div: 971.0ms (27.8% of total)

ival-mult: 917.0ms (26.3% of total)

ival-sub: 184.0ms (5.3% of total)

const: 35.0ms (1% of total)

Bogosity

preprocess122.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

811×	`distribute-lft-neg-in`
773×	`distribute-rgt-neg-in`
414×	`neg-sub0`
413×	`neg-mul-1`
344×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	2460
1	578	2428
2	1980	2340
3	4745	2320

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (pow.f64 (/.f64 (neg.f64 d) h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 (neg.f64 d) l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) (neg.f64 d))) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (pow.f64 (/.f64 d (neg.f64 h)) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 (neg.f64 h) l))))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d (neg.f64 l)) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h (neg.f64 l)))))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 (neg.f64 M) D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M (neg.f64 D)) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))
(neg.f64 (.f64 (.f64 (pow.f64 (/.f64 (neg.f64 d) h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 (neg.f64 d) l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) (neg.f64 d))) #s(literal 2 binary64))) (/.f64 h l)))))
(neg.f64 (.f64 (.f64 (pow.f64 (/.f64 d (neg.f64 h)) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 (neg.f64 h) l)))))
(neg.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d (neg.f64 l)) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h (neg.f64 l))))))
(neg.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 (neg.f64 M) D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l)))))
(neg.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M (neg.f64 D)) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l)))))
(.f64 (.f64 (pow.f64 (/.f64 h d) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 h l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) h)) #s(literal 2 binary64))) (/.f64 d l))))
(.f64 (.f64 (pow.f64 (/.f64 l h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 l d) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) l)) #s(literal 2 binary64))) (/.f64 h d))))
(.f64 (.f64 (pow.f64 (/.f64 M h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 M l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 d D) (.f64 #s(literal 2 binary64) M)) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (pow.f64 (/.f64 D h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 D l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M d) (.f64 #s(literal 2 binary64) D)) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 l h))))
(.f64 (.f64 (pow.f64 (/.f64 d M) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 h D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 M l))))
(.f64 (.f64 (pow.f64 (/.f64 d D) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M h) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 D l))))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d M) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 l D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h M))))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d D) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M l) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h D))))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 D M) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))

Outputs
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (*.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) (/.f64 h l)))))
(.f64 (sqrt.f64 (/.f64 d l)) (.f64 (sqrt.f64 (/.f64 d h)) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 h l) (.f64 (pow.f64 (*.f64 D (/.f64 (/.f64 M #s(literal 2 binary64)) d)) #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 M (/.f64 D d))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 h l)) #s(literal 1 binary64))))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (*.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) (/.f64 h l)))))
(.f64 (sqrt.f64 (/.f64 d l)) (.f64 (sqrt.f64 (/.f64 d h)) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 h l) (.f64 (pow.f64 (*.f64 D (/.f64 (/.f64 M #s(literal 2 binary64)) d)) #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 M (/.f64 D d))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 h l)) #s(literal 1 binary64))))
(.f64 (.f64 (pow.f64 (/.f64 (neg.f64 d) h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 (neg.f64 d) l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) (neg.f64 d))) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (sqrt.f64 (/.f64 d (neg.f64 h))) (sqrt.f64 (/.f64 d (neg.f64 l)))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 h l) (.f64 #s(literal 1/2 binary64) (pow.f64 (*.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D (neg.f64 d))) #s(literal 2 binary64))))))
(.f64 (.f64 (sqrt.f64 (/.f64 d (neg.f64 h))) (sqrt.f64 (/.f64 d (neg.f64 l)))) (-.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 d #s(literal -2 binary64))) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 h l)))))
(.f64 (.f64 (sqrt.f64 (/.f64 d (neg.f64 h))) (sqrt.f64 (/.f64 d (neg.f64 l)))) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (sqrt.f64 (/.f64 d (neg.f64 h))) (sqrt.f64 (/.f64 d (neg.f64 l)))) (fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 M (/.f64 D d))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 h l)) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 (/.f64 d (neg.f64 h)) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 (neg.f64 h) l))))
(.f64 (sqrt.f64 (/.f64 d (neg.f64 h))) (.f64 (sqrt.f64 (/.f64 d l)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (*.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) (/.f64 h (neg.f64 l)))))))
(.f64 (sqrt.f64 (/.f64 d (neg.f64 h))) (.f64 (sqrt.f64 (/.f64 d l)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (*.f64 D (/.f64 (/.f64 M #s(literal 2 binary64)) d)) #s(literal 2 binary64)) (/.f64 h l))))))
(.f64 (sqrt.f64 (/.f64 d (neg.f64 h))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) (/.f64 h l)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 d (neg.f64 h))) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (*.f64 M (/.f64 D d))) #s(literal 2 binary64)) (/.f64 h l)) #s(literal 1 binary64))))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d (neg.f64 l)) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h (neg.f64 l)))))
(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d (neg.f64 l))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (*.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) (/.f64 h (neg.f64 l)))))))
(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d (neg.f64 l))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (*.f64 D (/.f64 (/.f64 M #s(literal 2 binary64)) d)) #s(literal 2 binary64)) (/.f64 h l))))))
(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d (neg.f64 l)))) (fma.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) (/.f64 h l)) #s(literal 1 binary64)))
(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d (neg.f64 l)))) (fma.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (*.f64 M (/.f64 D d))) #s(literal 2 binary64)) (/.f64 h l)) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 (neg.f64 M) D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (*.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) (/.f64 h l)))))
(.f64 (sqrt.f64 (/.f64 d l)) (.f64 (sqrt.f64 (/.f64 d h)) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 h l) (.f64 (pow.f64 (*.f64 D (/.f64 (/.f64 M #s(literal 2 binary64)) d)) #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
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(.f64 (sqrt.f64 (/.f64 d D)) (.f64 (sqrt.f64 (/.f64 d h)) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 h D) (.f64 (pow.f64 (*.f64 l (/.f64 (/.f64 M #s(literal 2 binary64)) d)) #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d D))) (fma.f64 (/.f64 h D) (.f64 (pow.f64 (.f64 l (/.f64 M (*.f64 d #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 D M) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))
(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (*.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) (/.f64 h l)))))
(.f64 (sqrt.f64 (/.f64 d l)) (.f64 (sqrt.f64 (/.f64 d h)) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 h l) (.f64 (pow.f64 (*.f64 D (/.f64 (/.f64 M #s(literal 2 binary64)) d)) #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 (/.f64 M #s(literal 2 binary64)) (/.f64 D d)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 M (/.f64 D d))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 h l)) #s(literal 1 binary64))))

Symmetry

(abs M)

(abs D)

(sort M D)

explain429.0ms (5.8%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
65	129	(1.3263962035602875e+250 5.0448174019962377e+76 8.390669128250104e+72 1.5233222271573854e-215 1.0014375358138558e-129)	0	-	`(pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))`
61	126	(1.3263962035602875e+250 5.0448174019962377e+76 8.390669128250104e+72 1.5233222271573854e-215 1.0014375358138558e-129)	0	-	`(pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))`
46	0	-	1	(383320275130562500.0 1.1336125463527791e-77 4.433258375525156e+241 5.619456469222206e+20 7.110504211909721e+60)	`(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))`
26	0	-	2	(-2.1811776192491207e-229 -5.905170835803846e+71 -6.535781214166859e-164 3.914322725689442e-197 7.873347245454619e-116)	`(/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d))`
19	0	-	0	-	`(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))`
0	0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (*.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64)))`
0	0	-	0	-	`h`
0	0	-	0	-	`M`
0	0	-	0	-	`(*.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))))`
0	0	-	0	-	`l`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l)))`
0	0	-	0	-	`(/.f64 d h)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))`
0	0	-	0	-	`(*.f64 M D)`
0	0	-	0	-	`(/.f64 d l)`
0	0	-	0	-	`d`
0	0	-	0	-	`#s(literal 1 binary64)`
0	41	(8.338344819659082e-113 4.1359981370075833e+117 4.610365885074507e-179 2.1501173683759785e-259 2.4426170535644164e+47)	0	-	`(pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))`
0	0	-	0	-	`D`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) d)`
0	0	-	0	-	`(/.f64 h l)`

Results

316.0ms

512×

256

valid

Compiler

Compiled 360 to 68 computations (81.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 264.0ms

ival-div: 193.0ms (73.1% of total)

ival-pow: 44.0ms (16.7% of total)

ival-mult: 24.0ms (9.1% of total)

ival-sub: 3.0ms (1.1% of total)

const: 1.0ms (0.4% of total)

eval0.0ms (0%)

Compiler: Compiled 5 to 5 computations (0% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	70.4%	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 M D) (.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))

Status

Accuracy

Program

70.4%

(*.f64 (*.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 M D) (*.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))

Compiler

Compiled 80 to 44 computations (45% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative`
8×	`sub-neg`
8×	`+-commutative`
7×	`neg-sub0`
7×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	112
1	48	112
2	65	112
3	79	112
4	91	112
5	98	112
6	100	112

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 (*.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 M D) (*.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))

Outputs

(*.f64 (*.f64 (pow.f64 (/.f64 d h) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))) (pow.f64 (/.f64 d l) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 M D) (*.f64 #s(literal 2 binary64) d)) #s(literal 2 binary64))) (/.f64 h l))))

(*.f64 (*.f64 (pow.f64 (/.f64 d h) #s(literal 1/2 binary64)) (pow.f64 (/.f64 d l) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 (*.f64 M D) (*.f64 d #s(literal 2 binary64))) #s(literal 2 binary64))) (/.f64 h l))))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess37.0ms (0.5%)

Remove

(sort M D)

(abs D)

(abs M)

Compiler

Compiled 556 to 352 computations (36.7% saved)

Henrywood and Agarwal, Equation (12)

analyze1.0s (13.8%)

sample5.8s (78.1%)

preprocess122.0ms (1.6%)

explain429.0ms (5.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

soundness0.0ms (0%)

preprocess37.0ms (0.5%)

end0.0ms (0%)

Profiling