Metrics for Falkner and Boettcher, Appendix B, 1

analyze420.0ms (6.3%)

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%	100%	0%	0%	0%	0%	3
0%	0%	100%	0%	0%	0%	0%	4
0%	0%	100%	0%	0%	0%	0%	5
0%	0%	100%	0%	0%	0%	0%	6
0%	0%	100%	0%	0%	0%	0%	7
0%	0%	100%	0%	0%	0%	0%	8
0%	0%	100%	0%	0%	0%	0%	9
0%	0%	100%	0%	0%	0%	0%	10
0%	0%	100%	0%	0%	0%	0%	11
0%	0%	100%	0%	0%	0%	0%	12

Compiler

Compiled 16 to 10 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 220.0ms

ival-mult: 88.0ms (40% of total)

ival-acos: 49.0ms (22.3% of total)

ival-sub: 47.0ms (21.3% of total)

ival-div: 30.0ms (13.6% of total)

const: 5.0ms (2.3% of total)

backward-pass: 2.0ms (0.9% of total)

sample4.5s (67.8%)

Results

709.0ms	8156×	0	invalid
1.5s	3576×	3	valid
843.0ms	2217×	1	valid
774.0ms	2109×	2	valid
33.0ms	354×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.5s

ival-acos: 636.0ms (25.1% of total)

ival-mult: 571.0ms (22.6% of total)

ival-sub: 459.0ms (18.1% of total)

ival-div: 422.0ms (16.7% of total)

backward-pass: 388.0ms (15.3% of total)

const: 55.0ms (2.2% of total)

Bogosity

preprocess454.0ms (6.8%)

Algorithm

2×	egg-herbie

Rules

8668×	`accelerator-lowering-fma.f32`
8668×	`accelerator-lowering-fma.f64`
2288×	`-lowering-.f32`
2288×	`-lowering-.f64`
2162×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	43
1	58	43
2	171	43
3	620	43
4	2458	43
5	4477	43
6	5330	43
7	6281	43
8	7284	43
9	7894	43
0	9	14
1	29	14
2	74	14
3	200	14
4	575	14
5	1232	14
6	2488	14
7	3858	14
8	5676	14
9	7330	14
10	7885	14
0	8099	12

Stop Event

1×	iter limit
1×	node limit
1×	node limit

Calls

Call 1

Inputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

Outputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))

Call 2

Inputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(acos (/ (- 1 (* 5 (* (neg v) (neg v)))) (- (* (neg v) (neg v)) 1)))
(neg (acos (/ (- 1 (* 5 (* (neg v) (neg v)))) (- (* (neg v) (neg v)) 1))))

Outputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(acos (/ (+ 1 (* v (* v -5))) (+ (* v v) -1)))
(acos (/ (- 1 (* 5 (* (neg v) (neg v)))) (- (* (neg v) (neg v)) 1)))
(acos (/ (+ 1 (* v (* v -5))) (+ (* v v) -1)))
(neg (acos (/ (- 1 (* 5 (* (neg v) (neg v)))) (- (* (neg v) (neg v)) 1))))
(neg (acos (/ (+ 1 (* v (* v -5))) (+ (* v v) -1))))

Symmetry

(abs v)

explain321.0ms (4.8%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
14	241	(1.1174602031076003e-199)	-	`(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v)))`
0	0	-	-	`(-.f64 (*.f64 v v) #s(literal 1 binary64))`
0	0	-	-	`v`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64)))`
0	0	-	-	`(*.f64 v v)`
0	0	-	-	`#s(literal 5 binary64)`
0	0	-	-	`#s(literal 1 binary64)`
0	1	(7.187202868780392e-163)	-	`(.f64 #s(literal 5 binary64) (.f64 v v))`

Results

186.0ms	228×	3	valid
31.0ms	142×	1	valid
41.0ms	122×	2	valid
2.0ms	20×	0	valid

Compiler

Compiled 119 to 29 computations (75.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 183.0ms

ival-mult: 86.0ms (47% of total)

backward-pass: 30.0ms (16.4% of total)

ival-acos: 29.0ms (15.8% of total)

ival-sub: 18.0ms (9.8% of total)

ival-div: 17.0ms (9.3% of total)

const: 3.0ms (1.6% of total)

eval0.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.8%	(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))

Compiler

Compiled 15 to 9 computations (40% saved)

localize492.0ms (7.4%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	#s(literal 1 binary64)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v)))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64)))
✓	cost-diff	0	(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
✓	accuracy	100.0%	(*.f64 v v)
✓	accuracy	100.0%	(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64)))
✓	accuracy	99.7%	(.f64 #s(literal 5 binary64) (.f64 v v))
✓	accuracy	98.8%	(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))

Rules

8668×	`accelerator-lowering-fma.f32`
8668×	`accelerator-lowering-fma.f64`
2288×	`-lowering-.f32`
2288×	`-lowering-.f64`
2162×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	50
1	29	50
2	74	50
3	200	50
4	575	50
5	1232	50
6	2488	50
7	3858	50
8	5676	50
9	7330	50
10	7885	50
0	8099	44

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
(- 1 (* 5 (* v v)))
1
(* 5 (* v v))
5
(* v v)
v
(- (* v v) 1)

Outputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))
(- 1 (* 5 (* v v)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -5 binary64)))
1
#s(literal 1 binary64)
(* 5 (* v v))
(.f64 #s(literal 5 binary64) (.f64 v v))
5
#s(literal 5 binary64)
(* v v)
(*.f64 v v)
v
(- (* v v) 1)
(+.f64 (*.f64 v v) #s(literal -1 binary64))

Results

70.0ms	114×	3	valid
15.0ms	71×	1	valid
23.0ms	61×	2	valid
1.0ms	10×	0	valid

Compiler

Compiled 52 to 10 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

backward-pass: 14.0ms (23.7% of total)

ival-acos: 14.0ms (23.7% of total)

ival-mult: 12.0ms (20.3% of total)

ival-div: 10.0ms (16.9% of total)

ival-sub: 9.0ms (15.2% of total)

const: 1.0ms (1.7% of total)

series8.0ms (0.1%)

Counts

6 → 60

Calls

Call 1

Inputs
#<alt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))>
#<alt (* 5 (* v v))>
#<alt (/ (- 1 (* 5 (* v v))) (- (* v v) 1))>
#<alt (* v v)>
#<alt (- 1 (* 5 (* v v)))>
#<alt 1>

Outputs
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt -1>
#<alt (- (* 4 (pow v 2)) 1)>
#<alt (- (* (pow v 2) (+ 4 (* 4 (pow v 2)))) 1)>
#<alt (- (* (pow v 2) (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))) 1)>
#<alt -5>
#<alt (* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt -5>
#<alt (* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt 1>
#<alt (+ 1 (* -5 (pow v 2)))>
#<alt (+ 1 (* -5 (pow v 2)))>
#<alt (+ 1 (* -5 (pow v 2)))>
#<alt (* -5 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* -5 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	v	@	0	(* 5 (* v v))
0.0ms	v	@	inf	(* 5 (* v v))
0.0ms	v	@	inf	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.0ms	v	@	-inf	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.0ms	v	@	inf	(* v v)

rewrite457.0ms (6.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4946×	`accelerator-lowering-fma.f32`
4946×	`accelerator-lowering-fma.f64`
4582×	`-lowering-.f32`
4582×	`-lowering-.f64`
3506×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	43
1	64	43
2	524	43
3	6816	43
0	8164	38

Stop Event

1×	iter limit
1×	node limit

Falkner and Boettcher, Appendix B, 1

analyze420.0ms (6.3%)

sample4.5s (67.8%)

preprocess454.0ms (6.8%)

explain321.0ms (4.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize492.0ms (7.4%)

series8.0ms (0.1%)

rewrite457.0ms (6.8%)

end0.0ms (0%)

Profiling