Metrics for Falkner and Boettcher, Appendix B, 2

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)

sample999.0ms (71.5%)

Results

988.0ms	8256×	body	256	valid
1.0ms	9×	body	256	invalid

Bogosity

preprocess94.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

1628×	`div-sub`
1600×	`sub-neg`
1484×	`unsub-neg`
740×	`fma-def`
522×	`associate-/l*`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	25	114
1	69	114
2	146	106
3	380	106
4	968	106
5	2483	98
6	4719	98
7	5757	98
8	7472	98

Stop Event

1×	node limit

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)))

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

Symmetry

(abs v)

Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify75.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1476×	`div-sub`
1414×	`fma-neg`
1280×	`fma-def`
838×	`distribute-lft-in`
708×	`distribute-rgt-in`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	57
1	39	57
2	91	53
3	242	53
4	709	53
5	1666	49
6	2764	49
7	4993	49
8	7286	49

Stop Event

1×	node limit

Counts

1 → 7

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

eval2.0ms (0.2%)

Compiler: Compiled 126 to 90 computations (28.6% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	6	1	7
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	6	2	8

Accurracy

100.0%

Counts

8 → 1

Alt Table

Click to see full alt table

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

Accuracy

Program

▶

100.0%

(*.f64 (*.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 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 30 computations (25% saved)

localize69.0ms (5%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.7%	(.f64 3 (.f64 v v))

Compiler

Compiled 73 to 49 computations (32.9% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	v	@	0	(.f64 3 (.f64 v v))
0.0ms	v	@	inf	(.f64 3 (.f64 v v))
0.0ms	v	@	-inf	(.f64 3 (.f64 v v))

rewrite49.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1058×	`pow1`
1022×	`add-sqr-sqrt`
974×	`add-exp-log`
974×	`log1p-expm1-u`
974×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1382	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 3 (.f64 v v))

Outputs
(-.f64 (+.f64 1 (.f64 3 (.f64 v v))) 1)
(pow.f64 (.f64 3 (.f64 v v)) 1)
(pow.f64 (cbrt.f64 (.f64 3 (.f64 v v))) 3)
(pow.f64 (pow.f64 (.f64 3 (.f64 v v)) 3) 1/3)
(pow.f64 (*.f64 v (sqrt.f64 3)) 2)
(sqrt.f64 (*.f64 9 (pow.f64 v 4)))
(log.f64 (pow.f64 (exp.f64 3) (*.f64 v v)))
(cbrt.f64 (pow.f64 (.f64 3 (.f64 v v)) 3))
(expm1.f64 (log1p.f64 (.f64 3 (.f64 v v))))
(exp.f64 (log.f64 (.f64 3 (.f64 v v))))
(log1p.f64 (expm1.f64 (.f64 3 (.f64 v v))))

simplify55.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

2120×	`log-prod`
1106×	`distribute-rgt-in`
1092×	`distribute-lft-in`
796×	`associate-r`
682×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	299
1	90	299
2	320	299
3	2087	299
4	6927	299

Stop Event

1×	node limit

Counts

23 → 13

Calls

Call 1

Inputs
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(*.f64 3 (pow.f64 v 2))
(-.f64 (+.f64 1 (.f64 3 (.f64 v v))) 1)
(pow.f64 (.f64 3 (.f64 v v)) 1)
(pow.f64 (cbrt.f64 (.f64 3 (.f64 v v))) 3)
(pow.f64 (pow.f64 (.f64 3 (.f64 v v)) 3) 1/3)
(pow.f64 (*.f64 v (sqrt.f64 3)) 2)
(sqrt.f64 (*.f64 9 (pow.f64 v 4)))
(log.f64 (pow.f64 (exp.f64 3) (*.f64 v v)))
(cbrt.f64 (pow.f64 (.f64 3 (.f64 v v)) 3))
(expm1.f64 (log1p.f64 (.f64 3 (.f64 v v))))
(exp.f64 (log.f64 (.f64 3 (.f64 v v))))
(log1p.f64 (expm1.f64 (.f64 3 (.f64 v v))))

Outputs
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(*.f64 3 (pow.f64 v 2))
(.f64 3 (.f64 v v))
(-.f64 (+.f64 1 (.f64 3 (.f64 v v))) 1)
(.f64 3 (.f64 v v))
(pow.f64 (.f64 3 (.f64 v v)) 1)
(.f64 3 (.f64 v v))
(pow.f64 (cbrt.f64 (.f64 3 (.f64 v v))) 3)
(.f64 3 (.f64 v v))
(pow.f64 (pow.f64 (.f64 3 (.f64 v v)) 3) 1/3)
(.f64 3 (.f64 v v))
(pow.f64 (*.f64 v (sqrt.f64 3)) 2)
(.f64 3 (.f64 v v))
(sqrt.f64 (*.f64 9 (pow.f64 v 4)))
(.f64 3 (.f64 v v))
(log.f64 (pow.f64 (exp.f64 3) (*.f64 v v)))
(.f64 3 (.f64 v v))
(cbrt.f64 (pow.f64 (.f64 3 (.f64 v v)) 3))
(.f64 3 (.f64 v v))
(expm1.f64 (log1p.f64 (.f64 3 (.f64 v v))))
(.f64 3 (.f64 v v))
(exp.f64 (log.f64 (.f64 3 (.f64 v v))))
(.f64 3 (.f64 v v))
(log1p.f64 (expm1.f64 (.f64 3 (.f64 v v))))
(.f64 3 (.f64 v v))

eval5.0ms (0.3%)

Compiler: Compiled 274 to 203 computations (25.9% saved)

prune2.0ms (0.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	1	14

Accurracy

100.0%

Counts

14 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	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 30 computations (25% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	57
1	32	57
2	48	57
3	56	57
4	60	57

Stop Event

1×	done
1×	saturated

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)))

Compiler

Compiled 20 to 15 computations (25% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess34.0ms (2.4%)

Remove: (abs v)
Compiler: Compiled 120 to 90 computations (25% saved)

analyze4.0ms (0.3%)

sample999.0ms (71.5%)

preprocess94.0ms (6.8%)

simplify75.0ms (5.4%)

eval2.0ms (0.2%)

prune2.0ms (0.1%)

localize69.0ms (5%)

series1.0ms (0.1%)

rewrite49.0ms (3.5%)

simplify55.0ms (3.9%)

eval5.0ms (0.3%)

prune2.0ms (0.2%)

simplify5.0ms (0.3%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess34.0ms (2.4%)

Profiling