Metrics for Falkner and Boettcher, Appendix B, 2

analyze8.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample13.3s (95.7%)

Results

3.1s	8256×	valid-rival
766.0ms	8193×	valid-sollya
315.0ms	63×	exit-sollya
10.0ms	9×	invalid-sollya
2.0ms	9×	invalid-rival

Bogosity

preprocess453.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1731×	`fma-define`
509×	`distribute-lft-in`
502×	`fma-neg`
465×	`distribute-rgt-in`
435×	`unsub-neg`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	280
1	81	276
2	199	260
3	637	256
4	1910	244
5	4131	244
6	5472	244
7	5803	244
8	5857	244
9	5917	244
10	6013	244
11	7603	244

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 (neg.f64 v) (neg.f64 v)))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))
(neg.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 (neg.f64 v) (neg.f64 v)))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))))

Outputs
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -3 binary64) (.f64 v v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #s(literal 4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal -1/4 binary64))) (fma.f64 v v #s(literal -1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -3 binary64) (.f64 v v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #s(literal 4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal -1/4 binary64))) (fma.f64 v v #s(literal -1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 (neg.f64 v) (neg.f64 v)))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -3 binary64) (.f64 v v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v))) #s(literal 4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal -1/4 binary64))) (fma.f64 v v #s(literal -1 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal -1/4 binary64))))
(neg.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 (neg.f64 v) (neg.f64 v)))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -3 binary64) (.f64 v v))))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 v v))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 1 binary64))) #s(literal 4 binary64)) (+.f64 (.f64 v v) #s(literal -1 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 v v #s(literal -1 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal 4 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal 1/4 binary64))))

Symmetry

(abs v)

Compiler

Compiled 20 to 14 computations (30% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune19.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

Status

Accuracy

Program

100.0%

(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

Compiler

Compiled 40 to 28 computations (30% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative`
6×	`sub-neg`
6×	`+-commutative`
4×	`neg-sub0`
4×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	69
1	37	69
2	53	69
3	61	69
4	65	69

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

Outputs

(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

soundness1.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess108.0ms (0.8%)

Remove: (abs v)
Compiler: Compiled 160 to 112 computations (30% saved)

Falkner and Boettcher, Appendix B, 2

analyze8.0ms (0.1%)

sample13.3s (95.7%)

preprocess453.0ms (3.3%)

eval0.0ms (0%)

prune19.0ms (0.1%)

simplify6.0ms (0%)

soundness1.0ms (0%)

preprocess108.0ms (0.8%)

end0.0ms (0%)

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