Details

analyze4.0ms (0.3%)

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 16 computations (23.8% saved)

sample918.0ms (62.2%)

Results

907.0ms	8256×	body	256	valid
1.0ms	11×	body	256	invalid

Bogosity

preprocess77.0ms (5.2%)

Algorithm

2×	egg-herbie

Rules

1080×	`associate-+l-`
1068×	`fma-def`
1004×	`*-commutative`
836×	`fma-neg`
766×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	57
1	39	57
2	96	53
3	239	53
4	686	53
5	1771	49
6	2756	49
7	4678	49
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))

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

Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify77.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

1080×	`associate-+l-`
1068×	`fma-def`
1004×	`*-commutative`
836×	`fma-neg`
766×	`distribute-lft-in`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	57
1	39	57
2	96	53
3	239	53
4	686	53
5	1771	49
6	2756	49
7	4678	49

Stop Event

1×	node limit

Counts

1 → 9

Calls

Call 1

Inputs
(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))

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

eval3.0ms (0.2%)

Compiler: Compiled 163 to 117 computations (28.2% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	7	2	9
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	7	3	10

Error

100.0%

Counts

10 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	100.0%	(.f64 (/.f64 (sqrt.f64 2) 4) (.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 3 v) v))) (-.f64 1 (*.f64 v v))))
▶	100.0%	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))

Status

Error

Program

▶

100.0%

(*.f64 (/.f64 (sqrt.f64 2) 4) (*.f64 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 3 v) v))) (-.f64 1 (*.f64 v v))))

▶

100.0%

(*.f64 (*.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 40 to 31 computations (22.5% saved)

localize23.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	100.0%	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
✓	100.0%	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
✓	100.0%	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
✓	99.8%	(.f64 3 (.f64 v v))

Compiler

Compiled 72 to 48 computations (33.3% saved)

series27.0ms (1.8%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
22.0ms	v	@	inf	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
1.0ms	v	@	0	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
1.0ms	v	@	inf	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
0.0ms	v	@	0	(.f64 3 (.f64 v v))
0.0ms	v	@	-inf	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))

rewrite345.0ms (23.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1902×	`associate-*l/`
426×	`associate-/r*`
356×	`add-sqr-sqrt`
340×	`pow1`
340×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	132
1	367	112
2	4590	112

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 3 (.f64 v v))
(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))

Outputs
((((x +.f64 (.f64 3 (.f64 v v)) 0))) (((x +.f64 1 (-.f64 (.f64 3 (.f64 v v)) 1)))) (((x -.f64 (-.f64 1 (.f64 (.f64 -3 v) v)) 1))) (((x pow.f64 (.f64 3 (.f64 v v)) 1))) (((x pow.f64 (.f64 v (sqrt.f64 3)) 2))) (((x pow.f64 (cbrt.f64 (.f64 3 (.f64 v v))) 3))) (((x pow.f64 (.f64 27 (pow.f64 v 6)) 1/3))) (((x sqrt.f64 (.f64 9 (pow.f64 v 4))))) (((x log.f64 (pow.f64 (pow.f64 (exp.f64 v) v) 3)))) (((x log.f64 (+.f64 1 (expm1.f64 (.f64 3 (.f64 v v))))))) (((x cbrt.f64 (.f64 27 (pow.f64 v 6))))) (((x expm1.f64 (log1p.f64 (.f64 3 (.f64 v v)))))) (((x exp.f64 (log.f64 (.f64 3 (.f64 v v)))))) (((x exp.f64 (.f64 (log.f64 (.f64 3 (.f64 v v))) 1)))) (((x log1p.f64 (expm1.f64 (.f64 3 (*.f64 v v)))))))
((((x +.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)) (.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)) (.f64 v (neg.f64 v)))))) (((x +.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)) (.f64 (.f64 v (neg.f64 v)) (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)))))) (((x +.f64 (.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)) (.f64 v (neg.f64 v))) (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8))))) (((x +.f64 (.f64 (.f64 v (neg.f64 v)) (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8))) (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8))))) (((x -.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)) (-.f64 1 (.f64 v v))))) 1))) (((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)))) (-.f64 1 (.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)) (.f64 v (neg.f64 v))))))) (((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)))) (-.f64 1 (.f64 (.f64 v (neg.f64 v)) (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8))))))) (((x /.f64 (sqrt.f64 2) (/.f64 4 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v))))))) (((x /.f64 1 (/.f64 (/.f64 4 (sqrt.f64 2)) (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v))))))) (((x /.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (/.f64 (/.f64 4 (sqrt.f64 2)) (-.f64 1 (.f64 v v)))))) (((x /.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)) (/.f64 1 (-.f64 1 (.f64 v v)))))) (((x /.f64 (-.f64 1 (.f64 v v)) (/.f64 4 (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v)))))))) (((x /.f64 (pow.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/4) (/.f64 (/.f64 4 (sqrt.f64 2)) (.f64 (pow.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/4) (-.f64 1 (.f64 v v))))))) (((x /.f64 (cbrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (/.f64 (/.f64 4 (sqrt.f64 2)) (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v)))) (-.f64 1 (.f64 v v))))))) (((x /.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v))) (/.f64 4 (sqrt.f64 2))))) (((x /.f64 (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v)))) (/.f64 4 (-.f64 1 (.f64 v v)))))) (((x /.f64 (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v)))) (/.f64 (.f64 4 (+.f64 (.f64 v v) 1)) (-.f64 1 (pow.f64 v 4)))))) (((x /.f64 (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v)))) (/.f64 (.f64 4 (+.f64 (.f64 v v) (+.f64 1 (pow.f64 v 4)))) (-.f64 1 (pow.f64 v 6)))))) (((x /.f64 (-.f64 1 (pow.f64 v 4)) (/.f64 (+.f64 (.f64 v v) 1) (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)))))) (((x /.f64 (-.f64 1 (pow.f64 v 4)) (/.f64 (.f64 (+.f64 (.f64 v v) 1) 4) (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v)))))))) (((x /.f64 (-.f64 1 (pow.f64 v 6)) (/.f64 (+.f64 (.f64 v v) (+.f64 1 (pow.f64 v 4))) (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)))))) (((x /.f64 (-.f64 1 (pow.f64 v 6)) (/.f64 (.f64 (+.f64 (.f64 v v) (+.f64 1 (pow.f64 v 4))) 4) (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v)))))))) (((x /.f64 (neg.f64 (sqrt.f64 2)) (/.f64 -4 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v))))))) (((x /.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v)))) (/.f64 (/.f64 4 (sqrt.f64 2)) (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v)))))))) (((x /.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v)))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v))))) (/.f64 (/.f64 4 (sqrt.f64 2)) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v)))))))) (((x /.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (sqrt.f64 (-.f64 1 (.f64 v v)))) (/.f64 (/.f64 4 (sqrt.f64 2)) (sqrt.f64 (-.f64 1 (.f64 v v))))))) (((x /.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (pow.f64 (cbrt.f64 (-.f64 1 (.f64 v v))) 2)) (/.f64 (/.f64 4 (sqrt.f64 2)) (cbrt.f64 (-.f64 1 (.f64 v v))))))) (((x /.f64 (.f64 (sqrt.f64 (sqrt.f64 1/8)) (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v)))) (sqrt.f64 (/.f64 4 (sqrt.f64 2)))))) (((x /.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (pow.f64 v 4))) (.f64 (/.f64 4 (sqrt.f64 2)) (+.f64 (.f64 v v) 1))))) (((x /.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (pow.f64 v 6))) (.f64 (/.f64 4 (sqrt.f64 2)) (+.f64 (.f64 v v) (+.f64 1 (pow.f64 v 4))))))) (((x /.f64 (.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)) (-.f64 1 (pow.f64 v 4))) (+.f64 (.f64 v v) 1)))) (((x /.f64 (.f64 (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8)) (-.f64 1 (pow.f64 v 6))) (+.f64 (.f64 v v) (+.f64 1 (pow.f64 v 4)))))) (((x /.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v))))) 4))) (((x /.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v)))) 4))) (((x /.f64 (.f64 (neg.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 -3 v) v))) (-.f64 1 (.f64 v v)))) -4))) (((x /.f64 (.f64 (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v)))) (-.f64 1 (.f64 v v))) 4))) (((x /.f64 (.f64 (-.f64 1 (pow.f64 v 4)) (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8))) (+.f64 (.f64 v v) 1)))) (((x /.f64 (.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/8))) (+.f64 (.f64 v v) (+.f64 1 (pow.f64 v 4)))))) (((x /.f64 (.f64 (pow.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/4) (sqrt.f64 (-.f64 1 (.f64 v v)))) (/.f64 (/.f64 4 (sqrt.f64 2)) (.f64 (pow.f64 (+.f64 1 (.f64 (.f64 -3 v) v)) 1/4) (sqrt.f64 (-.f64 1 (.f64 v v)))))))) (((x /.f64 (.f64 (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v)))) (-.f64 1 (pow.f64 v 4))) (.f64 4 (+.f64 (.f64 v v) 1))))) (((x /.f64 (.f64 (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v)))) (-.f64 1 (pow.f64 v 6))) (.f64 4 (+.f64 (.f64 v v) (+.f64 1 (pow.f64 v 4))))))) (((x /.f64 (.f64 (-.f64 1 (pow.f64 v 4)) (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v))))) (.f64 (+.f64 (.f64 v v) 1) 4)))) (((x /.f64 (.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (.f64 2 (+.f64 1 (.f64 (.f64 -3 v) v))))) (.f64 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Details

analyze4.0ms (0.3%)

sample918.0ms (62.2%)

preprocess77.0ms (5.2%)

simplify77.0ms (5.2%)

eval3.0ms (0.2%)

prune2.0ms (0.1%)

localize23.0ms (1.6%)

series27.0ms (1.8%)

rewrite345.0ms (23.3%)

end0.0ms (0%)

Profiling