Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze108.0ms (4.8%)

Memory

28.3MiB live, 121.4MiB allocated; 10ms collecting garbage

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
25%	25%	75%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.8s (80.8%)

Memory

27.4MiB live, 1 666.6MiB allocated; 310ms collecting garbage

Samples

635.0ms	2 191×	2	valid
473.0ms	4 194×	0	valid
300.0ms	701×	3	valid
121.0ms	1 168×	1	valid
2.0ms	2×	4	valid

Precisions

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

ival-cos: 750.0ms (58.4% of total)

adjust: 227.0ms (17.7% of total)

ival-sin: 174.0ms (13.5% of total)

ival-div!: 76.0ms (5.9% of total)

ival-sub!: 57.0ms (4.4% of total)

Bogosity

explain158.0ms (7%)

Memory

-22.8MiB live, 172.8MiB allocated; 56ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
74	1	(3.90801471114056e+187)	1	(-0.15834780885146707)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
53	0	-	1	(-1.990726506038253e-160)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	74	3
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	52	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	52

Confusion

	Predicted +	Predicted -
+	125	1
-	1	129

Precision

0.9920634920634921

Recall

0.9920634920634921

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	125	1	0
-	1	2	127

Precision?

0.9767441860465116

Recall?

1.0

Freqs

test

number	freq
0	130
1	126

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

35.0ms	92×	1	valid
29.0ms	268×	0	valid
28.0ms	114×	2	valid
14.0ms	38×	3	valid

Compiler

Compiled 45 to 22 computations (51.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

ival-cos: 38.0ms (42.1% of total)

adjust: 33.0ms (36.6% of total)

ival-sin: 12.0ms (13.3% of total)

ival-div!: 4.0ms (4.4% of total)

ival-sub!: 3.0ms (3.3% of total)

preprocess40.0ms (1.8%)

Memory

-6.1MiB live, 40.3MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	44	13
2	124	12
3	273	12
4	706	12
5	2414	12

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Symmetry

(negabs x)

Compiler

Compiled 14 to 12 computations (14.3% saved)

rewrite54.0ms (2.4%)

Memory

10.6MiB live, 55.8MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	14
1	45	14
0	350	14

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

6 → 44

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

Outputs
(/.f64 (-.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))) (+.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (fma.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)) (*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 x))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (sin.f64 x)) (.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (sin.f64 x) (sin.f64 x)))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)))
(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(neg.f64 (-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))))
(neg.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x)))
(tan.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))))
(+.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(neg.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(+.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
#s(literal 1 binary64)
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
x
(sin.f64 x)

eval4.0ms (0.2%)

Memory: 9.0MiB live, 9.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 521 to 133 computations (74.5% saved)

prune1.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	1	39

Accuracy

100.0%

Counts

39 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 4 to 4 computations (0% saved)

rewrite21.0ms (0.9%)

Memory

8.5MiB live, 8.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
1	24	9
0	118	9

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

4 → 19

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)

Outputs
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (neg.f64 (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (tan.f64 (PI.f64)))))
(/.f64 (sin.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64)))) (cos.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(tan.f64 (+.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))) (PI.f64)))
(tan.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 x #s(literal 2 binary64))
(neg.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64)))
(neg.f64 (/.f64 x #s(literal -2 binary64)))
x
#s(literal 2 binary64)

eval2.0ms (0.1%)

Memory: 1.9MiB live, 1.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 128 to 51 computations (60.2% saved)

prune1.0ms (0.1%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	1	16

Accuracy

100.0%

Counts

16 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes3.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Accuracy

Total -29.1b remaining (-∞%)

Threshold costs -29.1b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Outputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))

Calls

2 calls:

1.0ms	x
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
100.0%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

derivations1.0ms (0.1%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 4 to 4 computations (0% saved)

preprocess39.0ms (1.7%)

Memory: -36.1MiB live, 17.6MiB allocated; 5ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 38 to 36 computations (5.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze108.0ms (4.8%)

sample1.8s (80.8%)

explain158.0ms (7%)

preprocess40.0ms (1.8%)

rewrite54.0ms (2.4%)

eval4.0ms (0.2%)

prune1.0ms (0.1%)

rewrite21.0ms (0.9%)

eval2.0ms (0.1%)

prune1.0ms (0.1%)

regimes3.0ms (0.1%)

derivations1.0ms (0.1%)

preprocess39.0ms (1.7%)

end0.0ms (0%)

Profiling