Metrics for Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A

analyze700.0ms (2%)

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
50%	49.9%	49.9%	0.2%	0%	0%	0%	4
50%	49.9%	49.9%	0.2%	0%	0%	0%	5
50%	49.9%	49.9%	0.2%	0%	0%	0%	6
50%	49.9%	49.9%	0.2%	0%	0%	0%	7
66.7%	49.9%	25%	0.2%	0%	25%	0%	8
66.7%	49.9%	25%	0.2%	0%	25%	0%	9
66.7%	49.9%	25%	0.2%	0%	25%	0%	10
66.7%	49.9%	25%	0.2%	0%	25%	0%	11
80%	49.9%	12.5%	0.2%	0%	37.4%	0%	12

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample34.0s (96.5%)

Results

3.1s	8256×	valid-rival
5.6s	5821×	invalid-sollya
533.0ms	4111×	valid-sollya
651.0ms	1991×	invalid-rival
1.6s	315×	exit-sollya

Bogosity

preprocess337.0ms (1%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac`
461×	`distribute-lft-in`
444×	`unsub-neg`
437×	`fma-define`
425×	`distribute-rgt-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	1056
1	209	1024
2	522	1016
3	1625	1008
4	4624	1008
5	7304	1008

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 (neg.f64 x) #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (neg.f64 y)) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 (neg.f64 z) #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 (neg.f64 t) (neg.f64 t)) #s(literal 2 binary64))))
(neg.f64 (.f64 (.f64 (-.f64 (.f64 (neg.f64 x) #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64)))))
(neg.f64 (.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (neg.f64 y)) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64)))))
(neg.f64 (.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 (neg.f64 z) #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64)))))
(neg.f64 (.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 (neg.f64 t) (neg.f64 t)) #s(literal 2 binary64)))))
(.f64 (.f64 (-.f64 (.f64 y #s(literal 1/2 binary64)) x) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 z #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 x #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 t #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 x x) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) z) (sqrt.f64 (.f64 y #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) t) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 y y) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 t #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 z z) #s(literal 2 binary64))))

Outputs
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (sqrt.f64 (exp.f64 (*.f64 t t))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (exp.f64 t) t)))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (sqrt.f64 (exp.f64 (*.f64 t t))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (exp.f64 t) t)))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(.f64 (.f64 (-.f64 (.f64 (neg.f64 x) #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (exp.f64 (.f64 t t))) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (fma.f64 (neg.f64 x) #s(literal 1/2 binary64) (neg.f64 y))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (.f64 (-.f64 (.f64 x #s(literal -1/2 binary64)) y) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (neg.f64 (fma.f64 x #s(literal 1/2 binary64) y))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (-.f64 (.f64 x #s(literal -1/2 binary64)) y)))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (neg.f64 y)) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (exp.f64 (.f64 t t))) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (neg.f64 y))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (*.f64 (fma.f64 x #s(literal 1/2 binary64) y) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (fma.f64 x #s(literal 1/2 binary64) y)))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 (neg.f64 z) #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (.f64 (sqrt.f64 (neg.f64 (.f64 z #s(literal 2 binary64)))) (sqrt.f64 (exp.f64 (*.f64 t t)))))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (sqrt.f64 (.f64 z #s(literal -2 binary64)))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 (neg.f64 t) (neg.f64 t)) #s(literal 2 binary64))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (sqrt.f64 (exp.f64 (*.f64 t t))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (exp.f64 t) t)))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(neg.f64 (.f64 (.f64 (-.f64 (.f64 (neg.f64 x) #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (exp.f64 (.f64 t t))) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (neg.f64 y))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (*.f64 (fma.f64 x #s(literal 1/2 binary64) y) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (fma.f64 x #s(literal 1/2 binary64) y)))
(neg.f64 (.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (neg.f64 y)) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (exp.f64 (.f64 t t))) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (fma.f64 (neg.f64 x) #s(literal 1/2 binary64) (neg.f64 y))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (.f64 (-.f64 (.f64 x #s(literal -1/2 binary64)) y) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (neg.f64 (fma.f64 x #s(literal 1/2 binary64) y))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (-.f64 (.f64 x #s(literal -1/2 binary64)) y)))
(neg.f64 (.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 (neg.f64 z) #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64)))))
(.f64 (neg.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (neg.f64 (.f64 z #s(literal 2 binary64)))))) (sqrt.f64 (exp.f64 (*.f64 t t))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (neg.f64 (sqrt.f64 (.f64 z #s(literal -2 binary64))))))
(.f64 (.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (sqrt.f64 (.f64 z #s(literal -2 binary64)))) (+.f64 y (.f64 x #s(literal -1/2 binary64))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (.f64 (sqrt.f64 (*.f64 z #s(literal -2 binary64))) (fma.f64 x #s(literal -1/2 binary64) y)))
(neg.f64 (.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 (neg.f64 t) (neg.f64 t)) #s(literal 2 binary64)))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (exp.f64 (*.f64 t t)))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (+.f64 y (.f64 x #s(literal -1/2 binary64)))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (fma.f64 x #s(literal -1/2 binary64) y)))
(.f64 (.f64 (-.f64 (.f64 y #s(literal 1/2 binary64)) x) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (exp.f64 (.f64 t t))) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) y) x)))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) y) x) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (-.f64 (.f64 #s(literal 1/2 binary64) y) x)))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) y) x)))
(.f64 (.f64 (-.f64 (.f64 z #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 x #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (exp.f64 (.f64 t t))) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) z) y) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) z) y) (sqrt.f64 (.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (-.f64 (.f64 #s(literal 1/2 binary64) z) y)))
(.f64 (.f64 (-.f64 (.f64 t #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 x x) #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) t) y)) (sqrt.f64 (exp.f64 (*.f64 x x))))
(.f64 (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) t) y)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) z) (sqrt.f64 (.f64 y #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (exp.f64 (.f64 t t))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) z) (sqrt.f64 (*.f64 y #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) z) (sqrt.f64 (.f64 y #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (.f64 (fma.f64 x #s(literal 1/2 binary64) (neg.f64 z)) (sqrt.f64 (*.f64 y #s(literal 2 binary64)))))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) t) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 y y) #s(literal 2 binary64))))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) t) (.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (sqrt.f64 (exp.f64 (*.f64 y y)))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) t) (sqrt.f64 (exp.f64 (*.f64 y y)))))
(.f64 (sqrt.f64 (.f64 z #s(literal 2 binary64))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) t) (pow.f64 (sqrt.f64 (exp.f64 y)) y)))
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 t #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 z z) #s(literal 2 binary64))))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) t)) (sqrt.f64 (exp.f64 (*.f64 z z)))))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) t)) (sqrt.f64 (pow.f64 (exp.f64 z) z))))
(.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) t)) (pow.f64 (sqrt.f64 (exp.f64 z)) z)))

Symmetry

(abs t)

Compiler

Compiled 21 to 15 computations (28.6% saved)

eval0.0ms (0%)

Compiler: Compiled 4 to 4 computations (0% saved)

prune3.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.0%	(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))

Compiler

Compiled 42 to 30 computations (28.6% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative`
2×	`sub-neg`
2×	`+-commutative`
1×	`neg-sub0`
1×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	66
1	29	66
2	34	66
3	36	66
4	37	66

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))

Outputs
(.f64 (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) y) (sqrt.f64 (.f64 z #s(literal 2 binary64)))) (exp.f64 (/.f64 (*.f64 t t) #s(literal 2 binary64))))

soundness3.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 21 to 15 computations (28.6% saved)

preprocess160.0ms (0.5%)

Remove: (abs t)
Compiler: Compiled 214 to 154 computations (28% saved)

Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A

analyze700.0ms (2%)

sample34.0s (96.5%)

preprocess337.0ms (1%)

eval0.0ms (0%)

prune3.0ms (0%)

simplify19.0ms (0.1%)

soundness3.0ms (0%)

preprocess160.0ms (0.5%)

end0.0ms (0%)

Profiling