Metrics for Kahan p13 Example 1

analyze5.0ms (0.1%)

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
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 37 to 29 computations (21.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

Operation ival-add, time spent: 1.0ms, 42.0% of total-time

Operation ival-mult, time spent: 1.0ms, 42.0% 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

sample3.0s (35.8%)

Results

2.5s	8255×	0	valid
0.0ms	1×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.8s

Operation ival-add, time spent: 1.0s, 55.0% of total-time

Operation ival-mult, time spent: 378.0ms, 21.0% of total-time

Operation ival-div, time spent: 377.0ms, 21.0% of total-time

Operation const, time spent: 69.0ms, 4.0% of total-time

Bogosity

preprocess2.6s (30.5%)

Algorithm

1×	egg-herbie

Rules

1406×	`fma-def`
1052×	`fma-neg`
824×	`neg-mul-1`
804×	`div-sub`
728×	`sub-neg`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t))))`
-	-	`(.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))`
-	-	`(+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t))))`
-	-	`(+.f64 1 t)`
-	-	`(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))`
-	-	`(*.f64 2 t)`
-	-	`t`
-	-	`2`
-	-	`(/.f64 (*.f64 2 t) (+.f64 1 t))`
-	-	`1`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	544
1	58	480
2	143	460
3	537	420
4	2544	416
5	6574	416

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))
(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))
(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))) (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))))) (+.f64 2 (.f64 (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))) (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))))))
(neg.f64 (/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))) (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))))) (+.f64 2 (.f64 (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))) (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t)))))))

Outputs
(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))
(/.f64 (+.f64 1 (.f64 (/.f64 2 (/.f64 (+.f64 1 t) t)) (/.f64 2 (/.f64 (+.f64 1 t) t)))) (+.f64 2 (.f64 (/.f64 2 (/.f64 (+.f64 1 t) t)) (/.f64 2 (/.f64 (+.f64 1 t) t)))))
(/.f64 (fma.f64 (/.f64 t (/.f64 (+.f64 1 t) 2)) (/.f64 t (/.f64 (+.f64 1 t) 2)) 1) (fma.f64 (/.f64 t (/.f64 (+.f64 1 t) 2)) (/.f64 t (/.f64 (+.f64 1 t) 2)) 2))
(/.f64 (+.f64 1 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))
(/.f64 (fma.f64 (/.f64 (/.f64 (.f64 t 4) (+.f64 1 t)) (+.f64 1 t)) t 1) (fma.f64 (/.f64 (/.f64 4 (+.f64 1 t)) (+.f64 1 t)) (.f64 t t) 2))
(/.f64 (fma.f64 t (.f64 (/.f64 4 (+.f64 1 t)) (/.f64 t (+.f64 1 t))) 1) (fma.f64 t (.f64 (/.f64 4 (+.f64 1 t)) (/.f64 t (+.f64 1 t))) 2))
(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))
(/.f64 (+.f64 1 (.f64 (/.f64 2 (/.f64 (+.f64 1 t) t)) (/.f64 2 (/.f64 (+.f64 1 t) t)))) (+.f64 2 (.f64 (/.f64 2 (/.f64 (+.f64 1 t) t)) (/.f64 2 (/.f64 (+.f64 1 t) t)))))
(/.f64 (fma.f64 (/.f64 t (/.f64 (+.f64 1 t) 2)) (/.f64 t (/.f64 (+.f64 1 t) 2)) 1) (fma.f64 (/.f64 t (/.f64 (+.f64 1 t) 2)) (/.f64 t (/.f64 (+.f64 1 t) 2)) 2))
(/.f64 (+.f64 1 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))
(/.f64 (fma.f64 (/.f64 (/.f64 (.f64 t 4) (+.f64 1 t)) (+.f64 1 t)) t 1) (fma.f64 (/.f64 (/.f64 4 (+.f64 1 t)) (+.f64 1 t)) (.f64 t t) 2))
(/.f64 (fma.f64 t (.f64 (/.f64 4 (+.f64 1 t)) (/.f64 t (+.f64 1 t))) 1) (fma.f64 t (.f64 (/.f64 4 (+.f64 1 t)) (/.f64 t (+.f64 1 t))) 2))
(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))) (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))))) (+.f64 2 (.f64 (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))) (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))))))
(/.f64 (+.f64 1 (.f64 (/.f64 2 (/.f64 (-.f64 1 t) (neg.f64 t))) (/.f64 2 (/.f64 (-.f64 1 t) (neg.f64 t))))) (+.f64 2 (.f64 (/.f64 2 (/.f64 (-.f64 1 t) (neg.f64 t))) (/.f64 2 (/.f64 (-.f64 1 t) (neg.f64 t))))))
(/.f64 (fma.f64 (/.f64 (.f64 t -2) (-.f64 1 t)) (/.f64 (.f64 t -2) (-.f64 1 t)) 1) (fma.f64 (/.f64 (.f64 t -2) (-.f64 1 t)) (/.f64 (.f64 t -2) (-.f64 1 t)) 2))
(/.f64 (+.f64 1 (/.f64 (/.f64 (.f64 t (.f64 t 4)) (-.f64 1 t)) (-.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (.f64 t (.f64 t 4)) (-.f64 1 t)) (-.f64 1 t))))
(/.f64 (+.f64 1 (/.f64 (/.f64 4 (-.f64 (/.f64 1 t) 1)) (-.f64 (/.f64 1 t) 1))) (+.f64 2 (/.f64 (/.f64 4 (-.f64 (/.f64 1 t) 1)) (-.f64 (/.f64 1 t) 1))))
(/.f64 (fma.f64 t (/.f64 (/.f64 -4 (+.f64 1 (/.f64 -1 t))) (-.f64 1 t)) 1) (fma.f64 t (/.f64 (/.f64 -4 (+.f64 1 (/.f64 -1 t))) (-.f64 1 t)) 2))
(neg.f64 (/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))) (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))))) (+.f64 2 (.f64 (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t))) (/.f64 (.f64 2 (neg.f64 t)) (+.f64 1 (neg.f64 t)))))))
(/.f64 (neg.f64 (+.f64 1 (.f64 (/.f64 2 (/.f64 (-.f64 1 t) (neg.f64 t))) (/.f64 2 (/.f64 (-.f64 1 t) (neg.f64 t)))))) (+.f64 2 (.f64 (/.f64 2 (/.f64 (-.f64 1 t) (neg.f64 t))) (/.f64 2 (/.f64 (-.f64 1 t) (neg.f64 t))))))
(neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 t -2) (-.f64 1 t)) (/.f64 (.f64 t -2) (-.f64 1 t)) 1) (fma.f64 (/.f64 (.f64 t -2) (-.f64 1 t)) (/.f64 (.f64 t -2) (-.f64 1 t)) 2)))
(/.f64 (-.f64 -1 (/.f64 (/.f64 (.f64 t (.f64 t 4)) (-.f64 1 t)) (-.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (.f64 t (.f64 t 4)) (-.f64 1 t)) (-.f64 1 t))))
(/.f64 (+.f64 -1 (/.f64 (/.f64 4 (-.f64 (/.f64 1 t) 1)) (+.f64 1 (/.f64 -1 t)))) (+.f64 2 (/.f64 (/.f64 4 (-.f64 (/.f64 1 t) 1)) (-.f64 (/.f64 1 t) 1))))
(/.f64 (fma.f64 (/.f64 4 (+.f64 1 (/.f64 -1 t))) (/.f64 t (-.f64 1 t)) -1) (fma.f64 t (/.f64 (/.f64 -4 (+.f64 1 (/.f64 -1 t))) (-.f64 1 t)) 2))

Compiler

Compiled 240 to 182 computations (24.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.1s

Operation ival-add, time spent: 981.0ms, 47.0% of total-time

Operation ival-mult, time spent: 541.0ms, 26.0% of total-time

Operation ival-div, time spent: 498.0ms, 24.0% of total-time

Operation const, time spent: 77.0ms, 4.0% of total-time

eval5.0ms (0.1%)

Compiler: Compiled 158 to 118 computations (25.3% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (+.f64 1 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))
▶	100.0%	(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))

Status

Accuracy

Program

▶

100.0%

(/.f64 (+.f64 1 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))

▶

100.0%

(/.f64 (+.f64 1 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))) (+.f64 2 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))))

Compiler

Compiled 68 to 52 computations (23.5% saved)

localize2.6s (31.2%)

Compiler: Compiled 200 to 147 computations (26.5% saved)
Precisions: Click to see histograms. Total time spent on operations: 2.3s
Operation ival-add, time spent: 1.3s, 56.0% of total-time
Operation ival-div, time spent: 597.0ms, 26.0% of total-time
Operation ival-mult, time spent: 340.0ms, 15.0% of total-time
Operation const, time spent: 77.0ms, 3.0% of total-time

eval0.0ms (0%)

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

prune3.0ms (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

100.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 1 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))
✓	100.0%	(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))

Status

Accuracy

Program

✓

100.0%

(/.f64 (+.f64 1 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))

✓

100.0%

(/.f64 (+.f64 1 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))) (+.f64 2 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))))

Compiler

Compiled 135 to 103 computations (23.7% saved)

regimes14.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs

(/.f64 (+.f64 1 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))

(/.f64 (+.f64 1 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))) (+.f64 2 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))))

Outputs
(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))

Calls

4 calls:

6.0ms	(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))
3.0ms	t
3.0ms	(/.f64 (*.f64 2 t) (+.f64 1 t))
2.0ms	(.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))

Results

Accuracy	Segments	Branch
100.0%	1	`t`
100.0%	1	`(/.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))) (+.f64 2 (.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (.f64 2 t) (+.f64 1 t)))))`
100.0%	1	`(.f64 (/.f64 (.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))`
100.0%	1	`(/.f64 (*.f64 2 t) (+.f64 1 t))`

Compiler

Compiled 62 to 47 computations (24.2% saved)

regimes3.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 (+.f64 1 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))

Outputs
(/.f64 (+.f64 1 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`t`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	242
1	35	242

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(/.f64 (+.f64 1 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))) (+.f64 2 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))))

(/.f64 (+.f64 1 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))

Outputs

(/.f64 (+.f64 1 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))) (+.f64 2 (*.f64 (/.f64 (*.f64 2 t) (+.f64 1 t)) (/.f64 (*.f64 2 t) (+.f64 1 t)))))

(/.f64 (+.f64 1 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))) (+.f64 2 (/.f64 (/.f64 (*.f64 t 4) (/.f64 (+.f64 1 t) t)) (+.f64 1 t))))

Compiler

Compiled 68 to 52 computations (23.5% saved)

soundness114.0ms (1.3%)

Rules

1406×	`fma-def`
1052×	`fma-neg`
824×	`neg-mul-1`
804×	`div-sub`
728×	`sub-neg`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	544
1	58	480
2	143	460
3	537	420
4	2544	416
5	6574	416

Stop Event

1×	node limit

Compiler

Compiled 312 to 240 computations (23.1% saved)

end0.0ms (0%)

preprocess59.0ms (0.7%)

Compiler: Compiled 206 to 158 computations (23.3% saved)

analyze5.0ms (0.1%)

sample3.0s (35.8%)

preprocess2.6s (30.5%)

eval5.0ms (0.1%)

prune2.0ms (0%)

localize2.6s (31.2%)

eval0.0ms (0%)

prune3.0ms (0%)

regimes14.0ms (0.2%)

regimes3.0ms (0%)

simplify4.0ms (0%)

soundness114.0ms (1.3%)

end0.0ms (0%)

preprocess59.0ms (0.7%)

Profiling