Metrics for Trigonometry A

analyze9.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
0%	0%	25%	75%	0%	0%	0%	1
50%	12.5%	12.5%	75%	0%	0%	0%	2
50%	12.5%	12.5%	75%	0%	0%	0%	3
75%	18.7%	6.2%	75%	0%	0%	0%	4
87.5%	21.8%	3.1%	75%	0%	0%	0%	5
93.8%	23.4%	1.6%	75%	0%	0%	0%	6
93.8%	23.4%	1.6%	75%	0%	0%	0%	7
96.9%	24.2%	0.8%	75%	0%	0%	0%	8
96.9%	24.2%	0.8%	75%	0%	0%	0%	9
98.4%	24.6%	0.4%	75%	0%	0%	0%	10
98.4%	24.6%	0.4%	75%	0%	0%	0%	11
99.2%	24.8%	0.2%	75%	0%	0%	0%	12

Compiler

Compiled 20 to 14 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

Operation ival-add, time spent: 1.0ms, 20.0% of total-time

Operation ival-mult, time spent: 1.0ms, 20.0% of total-time

Operation ival-cos, time spent: 1.0ms, 20.0% of total-time

Operation ival-sin, time spent: 1.0ms, 20.0% of total-time

Operation ival-<=, time spent: 1.0ms, 20.0% of total-time

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

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

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

sample1.7s (43.5%)

Results

1.5s	8251×	0	valid
1.0ms	2×	2	valid
2.0ms	2×	3	valid
0.0ms	1×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 898.0ms

Operation ival-sin, time spent: 227.0ms, 25.0% of total-time

Operation ival-cos, time spent: 187.0ms, 21.0% of total-time

Operation ival-add, time spent: 149.0ms, 17.0% of total-time

Operation ival-mult, time spent: 141.0ms, 16.0% of total-time

Operation ival-<=, time spent: 85.0ms, 9.0% of total-time

Operation ival-div, time spent: 68.0ms, 8.0% of total-time

Operation const, time spent: 29.0ms, 3.0% of total-time

Operation ival-and, time spent: 13.0ms, 1.0% of total-time

Bogosity

preprocess1.1s (29.8%)

Algorithm

1×	egg-herbie

Rules

2702×	`fma-def`
1284×	`div-sub`
856×	`times-frac`
776×	`distribute-lft-neg-in`
664×	`sub-neg`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(cos.f64 v)`
-	-	`(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))`
-	-	`v`
-	-	`(sin.f64 v)`
-	-	`(*.f64 e (sin.f64 v))`
-	-	`(*.f64 e (cos.f64 v))`
-	-	`e`
-	-	`(+.f64 1 (*.f64 e (cos.f64 v)))`
-	-	`1`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	35	339
1	77	303
2	147	303
3	311	303
4	836	281
5	2902	269
6	5180	257
7	6152	257
8	6430	257
9	6572	257
10	6606	257
11	7042	257

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
(/.f64 (.f64 (neg.f64 e) (sin.f64 v)) (+.f64 1 (.f64 (neg.f64 e) (cos.f64 v))))
(/.f64 (.f64 e (sin.f64 (neg.f64 v))) (+.f64 1 (.f64 e (cos.f64 (neg.f64 v)))))
(neg.f64 (/.f64 (.f64 (neg.f64 e) (sin.f64 v)) (+.f64 1 (.f64 (neg.f64 e) (cos.f64 v)))))
(neg.f64 (/.f64 (.f64 e (sin.f64 (neg.f64 v))) (+.f64 1 (.f64 e (cos.f64 (neg.f64 v))))))
(/.f64 (.f64 v (sin.f64 e)) (+.f64 1 (.f64 v (cos.f64 e))))

Outputs
(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
(*.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) e)
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
(/.f64 (sin.f64 v) (-.f64 (/.f64 1 e) (neg.f64 (cos.f64 v))))
(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))
(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))
(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
(*.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) e)
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
(/.f64 (sin.f64 v) (-.f64 (/.f64 1 e) (neg.f64 (cos.f64 v))))
(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))
(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))
(/.f64 (.f64 (neg.f64 e) (sin.f64 v)) (+.f64 1 (.f64 (neg.f64 e) (cos.f64 v))))
(/.f64 (.f64 (sin.f64 v) (neg.f64 e)) (+.f64 1 (.f64 (cos.f64 v) (neg.f64 e))))
(/.f64 (*.f64 e (neg.f64 (sin.f64 v))) (fma.f64 (cos.f64 v) (neg.f64 e) 1))
(*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) (neg.f64 e) 1)) (neg.f64 e))
(.f64 (sin.f64 v) (/.f64 (neg.f64 e) (-.f64 1 (.f64 e (cos.f64 v)))))
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 1 e)))
(/.f64 (.f64 e (sin.f64 (neg.f64 v))) (+.f64 1 (.f64 e (cos.f64 (neg.f64 v)))))
(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (neg.f64 (sin.f64 v))))
(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (neg.f64 (sin.f64 v))))
(*.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) (neg.f64 e))
(*.f64 (sin.f64 v) (/.f64 (neg.f64 e) (fma.f64 e (cos.f64 v) 1)))
(/.f64 (sin.f64 v) (-.f64 (/.f64 -1 e) (cos.f64 v)))
(neg.f64 (/.f64 (.f64 (neg.f64 e) (sin.f64 v)) (+.f64 1 (.f64 (neg.f64 e) (cos.f64 v)))))
(/.f64 (neg.f64 (.f64 (sin.f64 v) (neg.f64 e))) (+.f64 1 (.f64 (cos.f64 v) (neg.f64 e))))
(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 (cos.f64 v) (neg.f64 e) 1))
(*.f64 (/.f64 e (fma.f64 (cos.f64 v) (neg.f64 e) 1)) (sin.f64 v))
(.f64 (sin.f64 v) (/.f64 e (-.f64 1 (.f64 e (cos.f64 v)))))
(/.f64 (sin.f64 v) (-.f64 (/.f64 1 e) (cos.f64 v)))
(neg.f64 (/.f64 (.f64 e (sin.f64 (neg.f64 v))) (+.f64 1 (.f64 e (cos.f64 (neg.f64 v))))))
(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
(*.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) e)
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
(/.f64 (sin.f64 v) (-.f64 (/.f64 1 e) (neg.f64 (cos.f64 v))))
(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))
(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))
(/.f64 (.f64 v (sin.f64 e)) (+.f64 1 (.f64 v (cos.f64 e))))
(/.f64 v (/.f64 (+.f64 1 (*.f64 v (cos.f64 e))) (sin.f64 e)))
(*.f64 (/.f64 v (fma.f64 v (cos.f64 e) 1)) (sin.f64 e))
(*.f64 (sin.f64 e) (/.f64 v (fma.f64 v (cos.f64 e) 1)))
(*.f64 v (/.f64 (sin.f64 e) (fma.f64 v (cos.f64 e) 1)))

Symmetry

(negabs v)

Compiler

Compiled 83 to 35 computations (57.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 768.0ms

Operation ival-cos, time spent: 306.0ms, 40.0% of total-time

Operation ival-sin, time spent: 265.0ms, 35.0% of total-time

Operation ival-add, time spent: 105.0ms, 14.0% of total-time

Operation ival-mult, time spent: 54.0ms, 7.0% of total-time

Operation ival-div, time spent: 25.0ms, 3.0% of total-time

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

eval1.0ms (0%)

Compiler: Compiled 60 to 29 computations (51.7% saved)

prune2.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
▶	99.6%	(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
▶	99.6%	(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))

Compiler

Compiled 36 to 25 computations (30.6% saved)

localize660.0ms (17.3%)

Compiler: Compiled 89 to 33 computations (62.9% saved)
Precisions: Click to see histograms. Total time spent on operations: 477.0ms
Operation ival-cos, time spent: 107.0ms, 22.0% of total-time
Operation ival-add, time spent: 100.0ms, 21.0% of total-time
Operation ival-div, time spent: 92.0ms, 19.0% of total-time
Operation ival-sin, time spent: 82.0ms, 17.0% of total-time
Operation ival-fma, time spent: 60.0ms, 13.0% of total-time
Operation ival-mult, time spent: 20.0ms, 4.0% of total-time
Operation const, time spent: 16.0ms, 3.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	3	3
Done	0	0
Total	3	3

Accuracy

99.8%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
✓	99.6%	(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
✓	99.6%	(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))

Compiler

Compiled 68 to 42 computations (38.2% saved)

regimes11.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

Inputs
(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))
(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))

Outputs
(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))

Calls

3 calls:

3.0ms	v
3.0ms	e
3.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))

Results

Accuracy	Segments	Branch
99.8%	1	`e`
99.8%	1	`v`
99.8%	1	`(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes7.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))

Outputs
(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))

Calls

2 calls:

4.0ms	e
2.0ms	v

Results

Accuracy	Segments	Branch
99.6%	1	`e`
99.6%	1	`v`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative`
4×	`*-commutative`
3×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	81
1	27	81

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))

Outputs
(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
(/.f64 (sin.f64 v) (+.f64 (/.f64 1 e) (cos.f64 v)))
(/.f64 (sin.f64 v) (+.f64 (cos.f64 v) (/.f64 1 e)))

Compiler

Compiled 24 to 17 computations (29.2% saved)

soundness288.0ms (7.5%)

Rules

2702×	`fma-def`
1284×	`div-sub`
856×	`times-frac`
776×	`distribute-lft-neg-in`
664×	`sub-neg`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	35	339
1	77	303
2	147	303
3	311	303
4	836	281
5	2902	269
6	5180	257
7	6152	257
8	6430	257
9	6572	257
10	6606	257
11	7042	257

Stop Event

1×	node limit

Compiler

Compiled 249 to 117 computations (53% saved)

end0.0ms (0%)

preprocess36.0ms (1%)

Remove: (negabs v)
Compiler: Compiled 148 to 98 computations (33.8% saved)

analyze9.0ms (0.2%)

sample1.7s (43.5%)

preprocess1.1s (29.8%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize660.0ms (17.3%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes11.0ms (0.3%)

regimes7.0ms (0.2%)

simplify3.0ms (0.1%)

soundness288.0ms (7.5%)

end0.0ms (0%)

preprocess36.0ms (1%)

Profiling