Metrics for From Warwick Tucker's Validated Numerics

analyze0.0ms (0%)

Algorithm

1×

random

Compiler

Compiled 45 to 32 computations (28.9% saved)

sample5.1s (69.6%)

Results

4.2s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 3.6s

ival-mult: 1.4s (39% of total)

ival-pow: 726.0ms (19.9% of total)

ival-add: 695.0ms (19.1% of total)

backward-pass: 370.0ms (10.2% of total)

ival-div: 187.0ms (5.1% of total)

ival-neg: 147.0ms (4% of total)

const: 98.0ms (2.7% of total)

Bogosity

preprocess32.0ms (0.4%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	1
0	50	1
0	50	1

Stop Event

1×	saturated
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (+ (+ (* 1335/4 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (neg (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 11/2 (pow 33096 8))) (/ 77617 (* 2 33096)))

Inputs

(+ (+ (+ (* 1335/4 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (neg (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 11/2 (pow 33096 8))) (/ 77617 (* 2 33096)))

Outputs
(+ (+ (+ (* 1335/4 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (neg (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 11/2 (pow 33096 8))) (/ 77617 (* 2 33096)))
#s(literal -54767/66192 binary64)

Outputs

(+ (+ (+ (* 1335/4 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (neg (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 11/2 (pow 33096 8))) (/ 77617 (* 2 33096)))

#s(literal -54767/66192 binary64)

Call 2

Inputs
(+ (+ (+ (* 1335/4 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (neg (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 11/2 (pow 33096 8))) (/ 77617 (* 2 33096)))

Inputs

(+ (+ (+ (* 1335/4 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (neg (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 11/2 (pow 33096 8))) (/ 77617 (* 2 33096)))

Outputs
(+ (+ (+ (* 1335/4 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (neg (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 11/2 (pow 33096 8))) (/ 77617 (* 2 33096)))
#s(literal -54767/66192 binary64)

Outputs

(+ (+ (+ (* 1335/4 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (neg (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 11/2 (pow 33096 8))) (/ 77617 (* 2 33096)))

#s(literal -54767/66192 binary64)

explain2.1s (28.9%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	(+.f64 (+.f64 (.f64 #s(literal 1335/4 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64))) (.f64 (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64)) (+.f64 (+.f64 (+.f64 (.f64 (.f64 #s(literal 11 binary64) (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64))) (.f64 #s(literal 33096 binary64) #s(literal 33096 binary64))) (neg.f64 (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64)))) (.f64 #s(literal -121 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 4 binary64)))) #s(literal -2 binary64)))) (*.f64 #s(literal 11/2 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 8 binary64))))
0	-	-	`#s(literal 11 binary64)`
0	-	-	`(.f64 (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64)) (+.f64 (+.f64 (+.f64 (.f64 (.f64 #s(literal 11 binary64) (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64))) (.f64 #s(literal 33096 binary64) #s(literal 33096 binary64))) (neg.f64 (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64)))) (*.f64 #s(literal -121 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 4 binary64)))) #s(literal -2 binary64)))`
0	-	-	`(*.f64 #s(literal 2 binary64) #s(literal 33096 binary64))`
0	-	-	`(+.f64 (+.f64 (+.f64 (.f64 (.f64 #s(literal 11 binary64) (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64))) (.f64 #s(literal 33096 binary64) #s(literal 33096 binary64))) (neg.f64 (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64)))) (*.f64 #s(literal -121 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 4 binary64)))) #s(literal -2 binary64))`
0	-	-	`(+.f64 (.f64 (.f64 #s(literal 11 binary64) (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64))) (.f64 #s(literal 33096 binary64) #s(literal 33096 binary64))) (neg.f64 (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64))))`
0	-	-	`(pow.f64 #s(literal 33096 binary64) #s(literal 4 binary64))`
0	-	-	`#s(literal -2 binary64)`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(*.f64 #s(literal 77617 binary64) #s(literal 77617 binary64))`
0	-	-	`#s(literal 6 binary64)`
0	-	-	`(neg.f64 (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64)))`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`(*.f64 #s(literal 11/2 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 8 binary64)))`
0	-	-	(+.f64 (+.f64 (+.f64 (.f64 #s(literal 1335/4 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64))) (.f64 (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64)) (+.f64 (+.f64 (+.f64 (.f64 (.f64 #s(literal 11 binary64) (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64))) (.f64 #s(literal 33096 binary64) #s(literal 33096 binary64))) (neg.f64 (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64)))) (.f64 #s(literal -121 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 4 binary64)))) #s(literal -2 binary64)))) (.f64 #s(literal 11/2 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 8 binary64)))) (/.f64 #s(literal 77617 binary64) (.f64 #s(literal 2 binary64) #s(literal 33096 binary64))))
0	-	-	`(/.f64 #s(literal 77617 binary64) (*.f64 #s(literal 2 binary64) #s(literal 33096 binary64)))`
0	-	-	`#s(literal -121 binary64)`
0	-	-	`(*.f64 #s(literal 1335/4 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64)))`
0	-	-	`#s(literal 1335/4 binary64)`
0	-	-	`(*.f64 #s(literal 33096 binary64) #s(literal 33096 binary64))`
0	-	-	`(pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64))`
0	-	-	`#s(literal 33096 binary64)`
0	-	-	`#s(literal 77617 binary64)`
0	-	-	(+.f64 (.f64 #s(literal 1335/4 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64))) (.f64 (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64)) (+.f64 (+.f64 (+.f64 (.f64 (.f64 #s(literal 11 binary64) (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64))) (.f64 #s(literal 33096 binary64) #s(literal 33096 binary64))) (neg.f64 (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64)))) (.f64 #s(literal -121 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 4 binary64)))) #s(literal -2 binary64))))
0	-	-	`#s(literal 11/2 binary64)`
0	-	-	`(*.f64 #s(literal -121 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 4 binary64)))`
0	-	-	`(.f64 #s(literal 11 binary64) (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64)))`
0	-	-	`(pow.f64 #s(literal 33096 binary64) #s(literal 8 binary64))`
0	-	-	`#s(literal 8 binary64)`
0	-	-	`(.f64 (.f64 #s(literal 11 binary64) (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64))) (.f64 #s(literal 33096 binary64) #s(literal 33096 binary64)))`
0	-	-	`(+.f64 (+.f64 (.f64 (.f64 #s(literal 11 binary64) (.f64 #s(literal 77617 binary64) #s(literal 77617 binary64))) (.f64 #s(literal 33096 binary64) #s(literal 33096 binary64))) (neg.f64 (pow.f64 #s(literal 33096 binary64) #s(literal 6 binary64)))) (*.f64 #s(literal -121 binary64) (pow.f64 #s(literal 33096 binary64) #s(literal 4 binary64))))`

Results

2.0s

512×

valid

Compiler

Compiled 572 to 95 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 241.0ms

ival-add: 75.0ms (31.2% of total)

ival-mult: 60.0ms (24.9% of total)

backward-pass: 47.0ms (19.5% of total)

ival-pow: 34.0ms (14.1% of total)

ival-div: 12.0ms (5% of total)

const: 7.0ms (2.9% of total)

ival-neg: 6.0ms (2.5% of total)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune0.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(literal -54767/66192 binary64)

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
-54767/66192

Outputs
-54767/66192
#s(literal -54767/66192 binary64)

localize12.0ms (0.2%)

Results

9.0ms

256×

valid

Compiler

Compiled 2 to 2 computations (0% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

...c/correct-round.rkt:119:19: 4.0ms (89.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite22.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Compiler: Compiled 0 to 0 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

100.0%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(literal -54767/66192 binary64)

Compiler

Compiled 46 to 33 computations (28.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(literal -54767/66192 binary64)

Outputs
#s(literal -54767/66192 binary64)

soundness5.0ms (0.1%)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	1
0	50	1

Stop Event

1×	done
1×	saturated
1×	saturated

Compiler

Compiled 1 to 1 computations (0% saved)

preprocess22.0ms (0.3%)

Compiler: Compiled 90 to 64 computations (28.9% saved)

From Warwick Tucker's Validated Numerics

analyze0.0ms (0%)

sample5.1s (69.6%)

preprocess32.0ms (0.4%)

explain2.1s (28.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize12.0ms (0.2%)

series0.0ms (0%)

rewrite22.0ms (0.3%)

simplify3.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

soundness5.0ms (0.1%)

preprocess22.0ms (0.3%)

end0.0ms (0%)

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