Metrics for From Rump in a 1983 paper, rewritten

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0%	100%	0%	0%	0%	0
100%	0%	0%	100%	0%	0%	0%	1

Compiler

Compiled 24 to 16 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

Operation ival-sub, time spent: 0.0ms, 0.0% of total-time

Operation ival-mult, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

Operation ival-pow, time spent: 0.0ms, 0.0% of total-time

Operation ival-and, time spent: 0.0ms, 0.0% of total-time

Operation ival-==, time spent: 0.0ms, 0.0% of total-time

sample1.4s (35.7%)

Results

1.3s	8255×	0	valid
0.0ms	1×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 723.0ms

Operation ival-sub, time spent: 289.0ms, 40.0% of total-time

Operation ival-mult, time spent: 179.0ms, 25.0% of total-time

Operation ival-==, time spent: 108.0ms, 15.0% of total-time

Operation ival-pow, time spent: 102.0ms, 14.0% of total-time

Operation const, time spent: 33.0ms, 5.0% of total-time

Operation ival-and, time spent: 13.0ms, 2.0% of total-time

Bogosity

preprocess1.1s (27.7%)

Algorithm

1×	egg-herbie

Rules

1006×	`fma-neg`
882×	`distribute-lft-neg-in`
756×	`distribute-rgt-neg-in`
734×	`unswap-sqr`
694×	`sub-neg`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(pow.f64 x 4)`
-	-	`(*.f64 y y)`
-	-	`y`
-	-	`(.f64 (.f64 y y) (-.f64 (*.f64 y y) 2))`
-	-	`9`
-	-	`(*.f64 9 (pow.f64 x 4))`
-	-	`4`
-	-	`(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))`
-	-	`2`
-	-	`(-.f64 (*.f64 y y) 2)`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	34	378
1	99	357
2	274	357
3	914	336
4	2508	336
5	4520	336
6	5967	336
7	6558	336
8	7091	336
9	7451	336
10	7780	308

Stop Event

1×	node limit

Calls

Call 1

Inputs
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))
(-.f64 (.f64 9 (pow.f64 (neg.f64 x) 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 (neg.f64 y) (neg.f64 y)) (-.f64 (.f64 (neg.f64 y) (neg.f64 y)) 2)))
(neg.f64 (-.f64 (.f64 9 (pow.f64 (neg.f64 x) 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2))))
(neg.f64 (-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 (neg.f64 y) (neg.f64 y)) (-.f64 (.f64 (neg.f64 y) (neg.f64 y)) 2))))
(-.f64 (.f64 9 (pow.f64 y 4)) (.f64 (.f64 x x) (-.f64 (.f64 x x) 2)))

Outputs
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 y (*.f64 y (fma.f64 y y -2))))
(fma.f64 9 (pow.f64 x 4) (*.f64 (pow.f64 y 2) (neg.f64 (fma.f64 y y -2))))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (fma.f64 y y -2) (pow.f64 y 2)))
(-.f64 (*.f64 9 (pow.f64 x 4)) (fma.f64 (pow.f64 y 2) -2 (pow.f64 y 4)))
(-.f64 (fma.f64 2 (pow.f64 y 2) (*.f64 9 (pow.f64 x 4))) (pow.f64 y 4))
(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 y (*.f64 y (fma.f64 y y -2))))
(fma.f64 9 (pow.f64 x 4) (*.f64 (pow.f64 y 2) (neg.f64 (fma.f64 y y -2))))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (fma.f64 y y -2) (pow.f64 y 2)))
(-.f64 (*.f64 9 (pow.f64 x 4)) (fma.f64 (pow.f64 y 2) -2 (pow.f64 y 4)))
(-.f64 (fma.f64 2 (pow.f64 y 2) (*.f64 9 (pow.f64 x 4))) (pow.f64 y 4))
(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))
(-.f64 (.f64 9 (pow.f64 (neg.f64 x) 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 y (*.f64 y (fma.f64 y y -2))))
(fma.f64 9 (pow.f64 x 4) (*.f64 (pow.f64 y 2) (neg.f64 (fma.f64 y y -2))))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (fma.f64 y y -2) (pow.f64 y 2)))
(-.f64 (*.f64 9 (pow.f64 x 4)) (fma.f64 (pow.f64 y 2) -2 (pow.f64 y 4)))
(-.f64 (fma.f64 2 (pow.f64 y 2) (*.f64 9 (pow.f64 x 4))) (pow.f64 y 4))
(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 (neg.f64 y) (neg.f64 y)) (-.f64 (.f64 (neg.f64 y) (neg.f64 y)) 2)))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 y (*.f64 y (fma.f64 y y -2))))
(fma.f64 9 (pow.f64 x 4) (*.f64 (pow.f64 y 2) (neg.f64 (fma.f64 y y -2))))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (fma.f64 y y -2) (pow.f64 y 2)))
(-.f64 (*.f64 9 (pow.f64 x 4)) (fma.f64 (pow.f64 y 2) -2 (pow.f64 y 4)))
(-.f64 (fma.f64 2 (pow.f64 y 2) (*.f64 9 (pow.f64 x 4))) (pow.f64 y 4))
(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))
(neg.f64 (-.f64 (.f64 9 (pow.f64 (neg.f64 x) 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2))))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 y (*.f64 y (fma.f64 y y -2))))
(fma.f64 9 (pow.f64 x 4) (*.f64 (pow.f64 y 2) (neg.f64 (fma.f64 y y -2))))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (fma.f64 y y -2) (pow.f64 y 2)))
(-.f64 (*.f64 9 (pow.f64 x 4)) (fma.f64 (pow.f64 y 2) -2 (pow.f64 y 4)))
(-.f64 (fma.f64 2 (pow.f64 y 2) (*.f64 9 (pow.f64 x 4))) (pow.f64 y 4))
(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))
(neg.f64 (-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 (neg.f64 y) (neg.f64 y)) (-.f64 (.f64 (neg.f64 y) (neg.f64 y)) 2))))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 y (*.f64 y (fma.f64 y y -2))))
(fma.f64 9 (pow.f64 x 4) (*.f64 (pow.f64 y 2) (neg.f64 (fma.f64 y y -2))))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (fma.f64 y y -2) (pow.f64 y 2)))
(-.f64 (*.f64 9 (pow.f64 x 4)) (fma.f64 (pow.f64 y 2) -2 (pow.f64 y 4)))
(-.f64 (fma.f64 2 (pow.f64 y 2) (*.f64 9 (pow.f64 x 4))) (pow.f64 y 4))
(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))
(-.f64 (.f64 9 (pow.f64 y 4)) (.f64 (.f64 x x) (-.f64 (.f64 x x) 2)))
(-.f64 (.f64 9 (pow.f64 y 4)) (.f64 x (*.f64 x (fma.f64 x x -2))))
(-.f64 (.f64 9 (pow.f64 y 4)) (.f64 (pow.f64 x 2) (fma.f64 x x -2)))
(fma.f64 9 (pow.f64 y 4) (-.f64 (*.f64 2 (pow.f64 x 2)) (pow.f64 x 4)))
(-.f64 (fma.f64 9 (pow.f64 y 4) (*.f64 2 (pow.f64 x 2))) (pow.f64 x 4))
(fma.f64 9 (pow.f64 y 4) (fma.f64 2 (pow.f64 x 2) (pow.f64 x 4)))

Symmetry

(abs x)

(abs y)

(negabs x)

(negabs y)

Compiler

Compiled 113 to 63 computations (44.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 588.0ms

Operation ival-sub, time spent: 272.0ms, 46.0% of total-time

Operation ival-mult, time spent: 146.0ms, 25.0% of total-time

Operation ival-pow, time spent: 140.0ms, 24.0% of total-time

Operation const, time spent: 30.0ms, 5.0% of total-time

eval2.0ms (0%)

Compiler: Compiled 85 to 63 computations (25.9% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.6%	(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))
▶	3.1%	(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))

Compiler

Compiled 32 to 23 computations (28.1% saved)

localize708.0ms (17.8%)

Compiler: Compiled 83 to 51 computations (38.6% saved)
Precisions: Click to see histograms. Total time spent on operations: 490.0ms
Operation ival-pow, time spent: 202.0ms, 41.0% of total-time
Operation ival-sub, time spent: 128.0ms, 26.0% of total-time
Operation ival-mult, time spent: 67.0ms, 14.0% of total-time
Operation ival-fma, time spent: 63.0ms, 13.0% of total-time
Operation const, time spent: 30.0ms, 6.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 2 to 2 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

9.6%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.6%	(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))
✓	3.1%	(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))

Compiler

Compiled 62 to 44 computations (29% saved)

regimes13.0ms (0.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))
(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))

Outputs
(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))

Calls

7 calls:

3.0ms	(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))
2.0ms	(*.f64 9 (pow.f64 x 4))
2.0ms	(.f64 (.f64 y y) (-.f64 (*.f64 y y) 2))
2.0ms	(*.f64 y y)
2.0ms	(pow.f64 x 4)

Results

Accuracy	Segments	Branch
9.6%	1	`x`
9.6%	1	`y`
9.6%	1	`(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))`
9.6%	1	`(*.f64 9 (pow.f64 x 4))`
9.6%	1	`(pow.f64 x 4)`
9.6%	1	`(.f64 (.f64 y y) (-.f64 (*.f64 y y) 2))`
9.6%	1	`(*.f64 y y)`

Compiler

Compiled 51 to 34 computations (33.3% saved)

regimes11.0ms (0.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))

Outputs
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))

Calls

7 calls:

2.0ms	(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))
2.0ms	(*.f64 9 (pow.f64 x 4))
2.0ms	(.f64 (.f64 y y) (-.f64 (*.f64 y y) 2))
1.0ms	(pow.f64 x 4)
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
3.1%	1	`x`
3.1%	1	`y`
3.1%	1	`(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))`
3.1%	1	`(*.f64 9 (pow.f64 x 4))`
3.1%	1	`(pow.f64 x 4)`
3.1%	1	`(.f64 (.f64 y y) (-.f64 (*.f64 y y) 2))`
3.1%	1	`(*.f64 y y)`

Compiler

Compiled 51 to 34 computations (33.3% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

148×	`unsub-neg`
82×	`neg-mul-1`
42×	`distribute-lft-neg-in`
38×	`distribute-neg-out`
28×	`distribute-lft-neg-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	102
1	31	102
2	49	102
3	62	102
4	82	102
5	88	102
6	93	102
7	122	102
8	164	102
9	168	102
10	185	102
11	253	102
12	314	102
13	315	102

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))
(-.f64 (.f64 9 (pow.f64 x 4)) (.f64 (.f64 y y) (-.f64 (.f64 y y) 2)))

Outputs

(fma.f64 9 (pow.f64 x 4) (fma.f64 2 (pow.f64 y 2) (pow.f64 y 4)))

(-.f64 (*.f64 9 (pow.f64 x 4)) (*.f64 (*.f64 y y) (-.f64 (*.f64 y y) 2)))

(+.f64 (*.f64 9 (pow.f64 x 4)) (*.f64 (*.f64 y y) (-.f64 2 (*.f64 y y))))

Compiler

Compiled 32 to 23 computations (28.1% saved)

soundness656.0ms (16.5%)

Rules

1006×	`fma-neg`
882×	`distribute-lft-neg-in`
756×	`distribute-rgt-neg-in`
734×	`unswap-sqr`
694×	`sub-neg`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	34	378
1	99	357
2	274	357
3	914	336
4	2508	336
5	4520	336
6	5967	336
7	6558	336
8	7091	336
9	7451	336
10	7780	308

Stop Event

1×	node limit

end0.0ms (0%)

preprocess50.0ms (1.3%)

Remove

(negabs y)

(negabs x)

(abs y)

(abs x)

Compiler

Compiled 454 to 352 computations (22.5% saved)

Iter	Nodes	Cost
0	21	102
1	31	102
2	49	102
3	62	102
4	82	102
5	88	102
6	93	102
7	122	102
8	164	102
9	168	102
10	185	102
11	253	102
12	314	102
13	315	102

Iter	Nodes	Cost
0	21	102
1	31	102
2	49	102
3	62	102
4	82	102
5	88	102
6	93	102
7	122	102
8	164	102
9	168	102
10	185	102
11	253	102
12	314	102
13	315	102

analyze0.0ms (0%)

sample1.4s (35.7%)

preprocess1.1s (27.7%)

eval2.0ms (0%)

prune2.0ms (0%)

localize708.0ms (17.8%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes13.0ms (0.3%)

regimes11.0ms (0.3%)

simplify12.0ms (0.3%)

soundness656.0ms (16.5%)

end0.0ms (0%)

preprocess50.0ms (1.3%)

Profiling

Iter	Nodes	Cost
0	21	102
1	31	102
2	49	102
3	62	102
4	82	102
5	88	102
6	93	102
7	122	102
8	164	102
9	168	102
10	185	102
11	253	102
12	314	102
13	315	102