Metrics for mixedcos

analyze156.0ms (3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
12.5%	12.5%	87.4%	0.1%	0%	0%	0%	4
18.8%	18.7%	81.1%	0.1%	0%	0%	0%	5
28.1%	28.1%	71.8%	0.1%	0%	0%	0%	6
42.2%	42.1%	57.7%	0.1%	0%	0%	0%	7
49.2%	49.1%	50.7%	0.1%	0%	0%	0%	8
57.4%	57.3%	42.5%	0.1%	0%	0%	0%	9
67%	66.9%	33%	0.1%	0%	0%	0%	10
71.8%	71.7%	28.2%	0.1%	0%	0%	0%	11
76.9%	76.8%	23.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 20 to 15 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

Operation ival-mult, time spent: 37.0ms, 42.0% of total-time

Operation ival-pow, time spent: 22.0ms, 25.0% of total-time

Operation ival-cos, time spent: 20.0ms, 23.0% of total-time

Operation ival-div, time spent: 5.0ms, 6.0% of total-time

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

sample1.6s (31.7%)

Results

1.1s	5648×	valid
426.0ms	2607×	infinite
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 705.0ms

Operation ival-mult, time spent: 252.0ms, 36.0% of total-time

Operation ival-cos, time spent: 209.0ms, 30.0% of total-time

Operation ival-pow, time spent: 150.0ms, 21.0% of total-time

Operation ival-div, time spent: 60.0ms, 9.0% of total-time

Operation const, time spent: 34.0ms, 5.0% of total-time

Bogosity

preprocess2.0s (38.4%)

Algorithm

1×	egg-herbie

Rules

1226×	`div-sub`
1120×	`unsub-neg`
740×	`associate-/l*`
728×	`distribute-lft-neg-in`
704×	`associate-r`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(.f64 (.f64 x (pow.f64 s 2)) x)`
-	-	`x`
-	-	`(pow.f64 s 2)`
-	-	`(*.f64 2 x)`
-	-	`(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))`
-	-	`c`
-	-	`(*.f64 x (pow.f64 s 2))`
-	-	`s`
-	-	`(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))`
-	-	`2`
-	-	`(pow.f64 c 2)`
-	-	`(cos.f64 (*.f64 2 x))`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	730
1	152	685
2	458	661
3	2534	661
4	6205	661

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 (neg.f64 x))) (.f64 (pow.f64 c 2) (.f64 (.f64 (neg.f64 x) (pow.f64 s 2)) (neg.f64 x))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 (neg.f64 c) 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 (neg.f64 s) 2)) x)))
(neg.f64 (/.f64 (cos.f64 (.f64 2 (neg.f64 x))) (.f64 (pow.f64 c 2) (.f64 (.f64 (neg.f64 x) (pow.f64 s 2)) (neg.f64 x)))))
(neg.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 (neg.f64 c) 2) (.f64 (.f64 x (pow.f64 s 2)) x))))
(neg.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 (neg.f64 s) 2)) x))))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 (pow.f64 x 2) (.f64 (.f64 c (pow.f64 s 2)) c)))
(/.f64 (cos.f64 (.f64 2 s)) (.f64 (pow.f64 c 2) (.f64 (.f64 s (pow.f64 x 2)) s)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (.f64 (.f64 x (pow.f64 c 2)) x)))

Outputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 x (.f64 x (pow.f64 s 2)))))
(/.f64 (cos.f64 (.f64 x -2)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 x (.f64 x (pow.f64 s 2)))))
(/.f64 (cos.f64 (.f64 x -2)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 (neg.f64 x))) (.f64 (pow.f64 c 2) (.f64 (.f64 (neg.f64 x) (pow.f64 s 2)) (neg.f64 x))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 x (.f64 x (pow.f64 s 2)))))
(/.f64 (cos.f64 (.f64 x -2)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 (neg.f64 c) 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 x (.f64 x (pow.f64 s 2)))))
(/.f64 (cos.f64 (.f64 x -2)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 (neg.f64 s) 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 x (.f64 x (pow.f64 s 2)))))
(/.f64 (cos.f64 (.f64 x -2)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(neg.f64 (/.f64 (cos.f64 (.f64 2 (neg.f64 x))) (.f64 (pow.f64 c 2) (.f64 (.f64 (neg.f64 x) (pow.f64 s 2)) (neg.f64 x)))))
(/.f64 (neg.f64 (cos.f64 (.f64 2 (neg.f64 x)))) (.f64 (pow.f64 c 2) (.f64 (neg.f64 x) (.f64 (pow.f64 s 2) (neg.f64 x)))))
(/.f64 (neg.f64 (/.f64 (cos.f64 (.f64 x -2)) (pow.f64 c 2))) (neg.f64 (neg.f64 (.f64 (pow.f64 s 2) (pow.f64 x 2)))))
(/.f64 (neg.f64 (cos.f64 (.f64 x -2))) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (neg.f64 (cos.f64 (.f64 2 x))) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (neg.f64 (/.f64 (cos.f64 (.f64 x -2)) (pow.f64 x 2))) (.f64 (pow.f64 c 2) (pow.f64 s 2)))
(neg.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 (neg.f64 c) 2) (.f64 (.f64 x (pow.f64 s 2)) x))))
(/.f64 (neg.f64 (cos.f64 (.f64 2 (neg.f64 x)))) (.f64 (pow.f64 c 2) (.f64 (neg.f64 x) (.f64 (pow.f64 s 2) (neg.f64 x)))))
(/.f64 (neg.f64 (/.f64 (cos.f64 (.f64 x -2)) (pow.f64 c 2))) (neg.f64 (neg.f64 (.f64 (pow.f64 s 2) (pow.f64 x 2)))))
(/.f64 (neg.f64 (cos.f64 (.f64 x -2))) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (neg.f64 (cos.f64 (.f64 2 x))) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (neg.f64 (/.f64 (cos.f64 (.f64 x -2)) (pow.f64 x 2))) (.f64 (pow.f64 c 2) (pow.f64 s 2)))
(neg.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 (neg.f64 s) 2)) x))))
(/.f64 (neg.f64 (cos.f64 (.f64 2 (neg.f64 x)))) (.f64 (pow.f64 c 2) (.f64 (neg.f64 x) (.f64 (pow.f64 s 2) (neg.f64 x)))))
(/.f64 (neg.f64 (/.f64 (cos.f64 (.f64 x -2)) (pow.f64 c 2))) (neg.f64 (neg.f64 (.f64 (pow.f64 s 2) (pow.f64 x 2)))))
(/.f64 (neg.f64 (cos.f64 (.f64 x -2))) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (neg.f64 (cos.f64 (.f64 2 x))) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (neg.f64 (/.f64 (cos.f64 (.f64 x -2)) (pow.f64 x 2))) (.f64 (pow.f64 c 2) (pow.f64 s 2)))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 (pow.f64 x 2) (.f64 (.f64 c (pow.f64 s 2)) c)))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 (pow.f64 x 2) (.f64 c (.f64 c (pow.f64 s 2)))))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (/.f64 (cos.f64 (.f64 2 c)) (.f64 (pow.f64 c 2) (pow.f64 s 2))) (pow.f64 x 2))
(/.f64 (cos.f64 (.f64 2 s)) (.f64 (pow.f64 c 2) (.f64 (.f64 s (pow.f64 x 2)) s)))
(/.f64 (cos.f64 (.f64 2 s)) (.f64 (pow.f64 c 2) (.f64 s (.f64 s (pow.f64 x 2)))))
(/.f64 (cos.f64 (.f64 2 s)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (.f64 (.f64 x (pow.f64 c 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 x (.f64 x (pow.f64 s 2)))))
(/.f64 (cos.f64 (.f64 x -2)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))

Symmetry

(abs x)

(abs c)

(abs s)

(sort c s)

Compiler

Compiled 139 to 92 computations (33.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.6s

Operation ival-mult, time spent: 681.0ms, 44.0% of total-time

Operation ival-cos, time spent: 635.0ms, 41.0% of total-time

Operation ival-pow, time spent: 176.0ms, 11.0% of total-time

Operation const, time spent: 36.0ms, 2.0% of total-time

Operation ival-div, time spent: 28.0ms, 2.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 51 to 38 computations (25.5% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.5%	(/.f64 (cos.f64 (.f64 x -2)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
▶	59.7%	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))

Compiler

Compiled 38 to 29 computations (23.7% saved)

localize1.3s (25.2%)

Compiler: Compiled 115 to 77 computations (33% saved)
Precisions: Click to see histograms. Total time spent on operations: 926.0ms
Operation ival-cos, time spent: 320.0ms, 35.0% of total-time
Operation ival-pow, time spent: 283.0ms, 31.0% of total-time
Operation ival-mult, time spent: 257.0ms, 28.0% of total-time
Operation const, time spent: 38.0ms, 4.0% of total-time
Operation ival-div, time spent: 27.0ms, 3.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	0	0
Total	2	2

Accuracy

59.7%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.5%	(/.f64 (cos.f64 (.f64 x -2)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))
✓	59.7%	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))

Compiler

Compiled 73 to 55 computations (24.7% saved)

regimes19.0ms (0.4%)

Accuracy

Total -3.4b remaining (-13.1%)

Threshold costs -3.4b (-13.1%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 x -2)) (.f64 (pow.f64 c 2) (*.f64 (pow.f64 s 2) (pow.f64 x 2))))

Outputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))

Calls

6 calls:

5.0ms	c
3.0ms	x
3.0ms	s
3.0ms	(pow.f64 s 2)
2.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))

Results

Accuracy	Segments	Branch
59.7%	1	`x`
59.7%	1	`c`
59.7%	1	`s`
59.7%	1	`(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))`
59.7%	1	`(pow.f64 c 2)`
59.7%	1	`(pow.f64 s 2)`

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	62
1	23	62

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))

Outputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 x (.f64 x (pow.f64 s 2)))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess61.0ms (1.2%)

Remove

(abs s)

(abs x)

Compiler

Compiled 532 to 392 computations (26.3% saved)

analyze156.0ms (3%)

sample1.6s (31.7%)

preprocess2.0s (38.4%)

eval1.0ms (0%)

prune2.0ms (0%)

localize1.3s (25.2%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes19.0ms (0.4%)

simplify2.0ms (0%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess61.0ms (1.2%)

Profiling