Metrics for Toniolo and Linder, Equation (2)

analyze764.0ms (10.3%)

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
0%	0%	99.8%	0.2%	0%	0%	0%	4
0%	0%	99.8%	0.2%	0%	0%	0%	5
0%	0%	99.8%	0.2%	0%	0%	0%	6
0%	0%	99.8%	0.2%	0%	0%	0%	7
0%	0%	99.8%	0.2%	0%	0%	0%	8
19.2%	18.7%	78.8%	0.2%	0%	2.3%	0%	9
19.4%	18.7%	77.6%	0.2%	0%	3.5%	0%	10
22.8%	21.8%	73.9%	0.2%	0%	4.1%	0%	11
23.3%	21.8%	71.8%	0.2%	0%	6.1%	0%	12

Compiler

Compiled 24 to 20 computations (16.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 575.0ms

Operation ival-pow, time spent: 351.0ms, 61.0% of total-time

Operation ival-div, time spent: 70.0ms, 12.0% of total-time

Operation ival-asin, time spent: 51.0ms, 9.0% of total-time

Operation ival-sqrt, time spent: 37.0ms, 6.0% of total-time

Operation ival-mult, time spent: 19.0ms, 3.0% of total-time

Operation ival-sub, time spent: 19.0ms, 3.0% of total-time

Operation ival-add, time spent: 18.0ms, 3.0% of total-time

Operation const, time spent: 10.0ms, 2.0% of total-time

sample3.9s (52.8%)

Results

1.9s	8255×	valid
1.7s	7173×	invalid
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 2.3s

Operation ival-pow, time spent: 514.0ms, 22.0% of total-time

Operation ival-sqrt, time spent: 449.0ms, 19.0% of total-time

Operation ival-div, time spent: 424.0ms, 18.0% of total-time

Operation ival-sub, time spent: 291.0ms, 12.0% of total-time

Operation ival-add, time spent: 278.0ms, 12.0% of total-time

Operation ival-asin, time spent: 182.0ms, 8.0% of total-time

Operation ival-mult, time spent: 121.0ms, 5.0% of total-time

Operation const, time spent: 80.0ms, 3.0% of total-time

Bogosity

preprocess1.8s (24.6%)

Algorithm

1×	egg-herbie

Rules

1832×	`fma-def`
1312×	`associate-r`
970×	`associate-l`
966×	`associate-/l*`
676×	`associate-*r/`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))`
-	-	`(*.f64 2 (pow.f64 (/.f64 t l) 2))`
-	-	`(pow.f64 (/.f64 Om Omc) 2)`
-	-	`(-.f64 1 (pow.f64 (/.f64 Om Omc) 2))`
-	-	`l`
-	-	`(/.f64 Om Omc)`
-	-	`(pow.f64 (/.f64 t l) 2)`
-	-	`(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))`
-	-	`Omc`
-	-	`(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))`
-	-	`(/.f64 t l)`
-	-	`t`
-	-	`Om`
-	-	`2`
-	-	`1`
-	-	`(+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	107	1140
1	236	1064
2	507	1064
3	1583	1064
4	7295	1064

Stop Event

1×	node limit

Calls

Call 1

Inputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 (neg.f64 t) l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t (neg.f64 l)) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (neg.f64 Om) Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om (neg.f64 Omc)) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 (neg.f64 t) l) 2)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t (neg.f64 l)) 2)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (neg.f64 Om) Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om (neg.f64 Omc)) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 l t) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 t Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 Om l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om t) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 Omc l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 l Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t Om) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om l) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t Omc) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Omc Om) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Outputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 (neg.f64 t) l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t (neg.f64 l)) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t (neg.f64 l)) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (neg.f64 Om) Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om (neg.f64 Omc)) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 (neg.f64 t) l) 2)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t (neg.f64 l)) 2)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t (neg.f64 l)) 2) 1)))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 (neg.f64 Om) Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 (neg.f64 t) l) 2)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om (neg.f64 Omc)) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 (neg.f64 t) l) 2)))))))
(neg.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 l t) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 l t) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 t Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 Om l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 t Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 Om l) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om t) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 Omc l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om t) 2)) (fma.f64 2 (pow.f64 (/.f64 Omc l) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 l Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t Om) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 l Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t Om) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om l) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t Omc) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om l) 2)) (fma.f64 2 (pow.f64 (/.f64 t Omc) 2) 1))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Omc Om) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Omc Om) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

Symmetry

(abs t)

(abs Om)

(abs Omc)

Compiler

Compiled 231 to 145 computations (37.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.3s

Operation ival-pow, time spent: 473.0ms, 35.0% of total-time

Operation ival-sub, time spent: 216.0ms, 16.0% of total-time

Operation ival-add, time spent: 204.0ms, 15.0% of total-time

Operation ival-div, time spent: 135.0ms, 10.0% of total-time

Operation ival-mult, time spent: 134.0ms, 10.0% of total-time

Operation ival-sqrt, time spent: 81.0ms, 6.0% of total-time

Operation const, time spent: 56.0ms, 4.0% of total-time

Operation ival-asin, time spent: 39.0ms, 3.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 22 to 18 computations (18.2% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	85.8%	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 23 to 19 computations (17.4% saved)

localize862.0ms (11.6%)

Compiler: Compiled 104 to 63 computations (39.4% saved)
Precisions: Click to see histograms. Total time spent on operations: 680.0ms
Operation ival-pow, time spent: 245.0ms, 36.0% of total-time
Operation ival-sub, time spent: 109.0ms, 16.0% of total-time
Operation ival-add, time spent: 98.0ms, 14.0% of total-time
Operation ival-div, time spent: 70.0ms, 10.0% of total-time
Operation ival-mult, time spent: 63.0ms, 9.0% of total-time
Operation ival-sqrt, time spent: 50.0ms, 7.0% of total-time
Operation const, time spent: 28.0ms, 4.0% of total-time
Operation ival-asin, time spent: 19.0ms, 3.0% of total-time

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	0	0
Total	1	1

Accuracy

85.8%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	85.8%	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 46 to 38 computations (17.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
4×	`sub-neg`
4×	`*-commutative`
3×	`1-exp`
2×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	69
1	33	69
2	37	69
3	39	69
4	40	69

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Outputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 23 to 19 computations (17.4% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess48.0ms (0.6%)

Remove

(abs Omc)

(abs Om)

(abs t)

Compiler

Compiled 368 to 304 computations (17.4% saved)

analyze764.0ms (10.3%)

sample3.9s (52.8%)

preprocess1.8s (24.6%)

eval1.0ms (0%)

prune1.0ms (0%)

localize862.0ms (11.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess48.0ms (0.6%)

Profiling