Metrics for logq (problem 3.4.3)

analyze3.0ms (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
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	75%	0%	0%	25%	0%	3
40%	25%	37.5%	0%	0%	37.5%	0%	4
66.7%	37.5%	18.7%	0%	0%	43.7%	0%	5
82.4%	43.7%	9.4%	0%	0%	46.9%	0%	6
90.9%	46.9%	4.7%	0%	0%	48.4%	0%	7
95.4%	48.4%	2.3%	0%	0%	49.2%	0%	8
97.7%	49.2%	1.2%	0%	0%	49.6%	0%	9
98.8%	49.6%	0.6%	0%	0%	49.8%	0%	10
99.4%	49.8%	0.3%	0%	0%	49.9%	0%	11
99.7%	49.9%	0.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample3.4s (64.5%)

Results

2.3s	4080×	body	1024	valid
487.0ms	2082×	body	512	valid
322.0ms	1689×	body	256	valid
232.0ms	405×	body	2048	valid
1.0ms	12×	body	256	invalid

Bogosity

preprocess312.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

8722×	`fma-def`
1220×	`unsub-neg`
1030×	`fma-neg`
668×	`associate-+r+`
656×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	73
1	37	57
2	70	57
3	148	57
4	377	57
5	984	57
6	1861	57
7	2532	57
8	3523	57
9	4766	57
10	5322	57
11	5483	57
12	5658	57
13	6107	57
14	7004	57
15	7072	57
16	7104	57
17	7124	57
18	7216	57
19	7357	57
20	7477	57
21	7477	57

Stop Event

1×	node limit

Calls

Call 1

Inputs
(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
(log.f64 (/.f64 (-.f64 1 (neg.f64 eps)) (+.f64 1 (neg.f64 eps))))

Outputs
(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
(log.f64 (/.f64 (-.f64 1 (neg.f64 eps)) (+.f64 1 (neg.f64 eps))))
(log.f64 (/.f64 (-.f64 1 (neg.f64 eps)) (-.f64 1 eps)))
(-.f64 (log1p.f64 eps) (log1p.f64 (neg.f64 eps)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
▶	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
▶	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
▶	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 32 to 24 computations (25% saved)

localize202.0ms (3.8%)

Localize:

Found 3 expressions with local error:

New	Accuracy	Program
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	100.0%	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
✓	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 39 to 22 computations (43.6% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
1.0ms	eps	@	0	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
0.0ms	eps	@	inf	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
0.0ms	eps	@	inf	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
0.0ms	eps	@	-inf	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

rewrite62.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1534×	`prod-diff`
920×	`log-prod`
676×	`fma-def`
448×	`pow-prod-up`
412×	`pow-exp`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	57
1	279	49
2	3805	3

Stop Event

1×	node limit

Counts

3 → 3

Calls

Call 1

Inputs
(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
(/.f64 (-.f64 1 eps) (+.f64 1 eps))
(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))

Outputs
0
1
0

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1482×	`fma-def`
1230×	`fma-neg`
1004×	`times-frac`
874×	`associate-*r/`
848×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	64	945
1	182	935
2	460	929
3	1293	917
4	3996	909

Stop Event

1×	node limit

Counts

39 → 66

Calls

Call 1

Inputs
(*.f64 -2 eps)
(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
(+.f64 (.f64 -2 eps) (+.f64 (.f64 -2/5 (pow.f64 eps 5)) (*.f64 -2/3 (pow.f64 eps 3))))
(+.f64 (.f64 -2 eps) (+.f64 (.f64 -2/5 (pow.f64 eps 5)) (+.f64 (.f64 -2/7 (pow.f64 eps 7)) (.f64 -2/3 (pow.f64 eps 3)))))
(log.f64 -1)
(-.f64 (log.f64 -1) (*.f64 2 (/.f64 1 eps)))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (+.f64 (.f64 2 (/.f64 1 eps)) (*.f64 2/5 (/.f64 1 (pow.f64 eps 5))))))
(log.f64 -1)
(-.f64 (log.f64 -1) (*.f64 2 (/.f64 1 eps)))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (+.f64 (.f64 2 (/.f64 1 eps)) (*.f64 2/5 (/.f64 1 (pow.f64 eps 5))))))
1
(+.f64 (*.f64 -2 eps) 1)
(+.f64 (.f64 -2 eps) (+.f64 (.f64 2 (pow.f64 eps 2)) 1))
(+.f64 (.f64 -2 eps) (+.f64 (.f64 2 (pow.f64 eps 2)) (+.f64 1 (*.f64 -2 (pow.f64 eps 3)))))
-1
(-.f64 (*.f64 2 (/.f64 1 eps)) 1)
(-.f64 (.f64 2 (/.f64 1 eps)) (+.f64 1 (.f64 2 (/.f64 1 (pow.f64 eps 2)))))
(-.f64 (+.f64 (.f64 2 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 eps 2)))))
-1
(-.f64 (*.f64 2 (/.f64 1 eps)) 1)
(-.f64 (.f64 2 (/.f64 1 eps)) (+.f64 1 (.f64 2 (/.f64 1 (pow.f64 eps 2)))))
(-.f64 (+.f64 (.f64 2 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 eps 2)))))
(*.f64 -2 eps)
(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
(+.f64 (.f64 -2 eps) (+.f64 (.f64 -2/5 (pow.f64 eps 5)) (*.f64 -2/3 (pow.f64 eps 3))))
(+.f64 (.f64 -2 eps) (+.f64 (.f64 -2/5 (pow.f64 eps 5)) (+.f64 (.f64 -2/7 (pow.f64 eps 7)) (.f64 -2/3 (pow.f64 eps 3)))))
(log.f64 -1)
(-.f64 (log.f64 -1) (*.f64 2 (/.f64 1 eps)))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (+.f64 (.f64 2 (/.f64 1 eps)) (*.f64 2/5 (/.f64 1 (pow.f64 eps 5))))))
(*.f64 -1 (log.f64 -1))
(-.f64 (.f64 -1 (log.f64 -1)) (.f64 2 (/.f64 1 eps)))
(-.f64 (.f64 -1 (log.f64 -1)) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (*.f64 2 (/.f64 1 eps))))
(-.f64 (.f64 -1 (log.f64 -1)) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (+.f64 (.f64 2 (/.f64 1 eps)) (.f64 2/5 (/.f64 1 (pow.f64 eps 5))))))
0
1
0

Outputs
(*.f64 -2 eps)
(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
(fma.f64 -2 eps (*.f64 -2/3 (pow.f64 eps 3)))
(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
(+.f64 (.f64 -2 eps) (+.f64 (.f64 -2/5 (pow.f64 eps 5)) (*.f64 -2/3 (pow.f64 eps 3))))
(fma.f64 -2 eps (fma.f64 -2/5 (pow.f64 eps 5) (*.f64 -2/3 (pow.f64 eps 3))))
(fma.f64 -2 eps (fma.f64 -2/3 (pow.f64 eps 3) (*.f64 -2/5 (pow.f64 eps 5))))
(+.f64 (.f64 -2 eps) (+.f64 (.f64 -2/5 (pow.f64 eps 5)) (+.f64 (.f64 -2/7 (pow.f64 eps 7)) (.f64 -2/3 (pow.f64 eps 3)))))
(fma.f64 -2 eps (fma.f64 -2/5 (pow.f64 eps 5) (fma.f64 -2/7 (pow.f64 eps 7) (*.f64 -2/3 (pow.f64 eps 3)))))
(fma.f64 -2 eps (fma.f64 -2/5 (pow.f64 eps 5) (fma.f64 -2/3 (pow.f64 eps 3) (*.f64 -2/7 (pow.f64 eps 7)))))
(fma.f64 -2 eps (fma.f64 -2/3 (pow.f64 eps 3) (fma.f64 -2/5 (pow.f64 eps 5) (*.f64 -2/7 (pow.f64 eps 7)))))
(log.f64 -1)
(-.f64 (log.f64 -1) (*.f64 2 (/.f64 1 eps)))
(-.f64 (log.f64 -1) (/.f64 2 eps))
(+.f64 (log.f64 -1) (/.f64 -2 eps))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))))
(-.f64 (log.f64 -1) (+.f64 (/.f64 2 eps) (/.f64 2/3 (pow.f64 eps 3))))
(+.f64 (-.f64 (log.f64 -1) (/.f64 2/3 (pow.f64 eps 3))) (/.f64 -2 eps))
(+.f64 (log.f64 -1) (+.f64 (/.f64 -2 eps) (/.f64 -2/3 (pow.f64 eps 3))))
(+.f64 (+.f64 (log.f64 -1) (/.f64 -2 eps)) (/.f64 -2/3 (pow.f64 eps 3)))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (+.f64 (.f64 2 (/.f64 1 eps)) (*.f64 2/5 (/.f64 1 (pow.f64 eps 5))))))
(-.f64 (log.f64 -1) (+.f64 (/.f64 2/3 (pow.f64 eps 3)) (+.f64 (/.f64 2 eps) (/.f64 2/5 (pow.f64 eps 5)))))
(-.f64 (-.f64 (log.f64 -1) (+.f64 (/.f64 2 eps) (/.f64 2/5 (pow.f64 eps 5)))) (/.f64 2/3 (pow.f64 eps 3)))
(+.f64 (log.f64 -1) (+.f64 (+.f64 (/.f64 -2 eps) (/.f64 -2/3 (pow.f64 eps 3))) (/.f64 -2/5 (pow.f64 eps 5))))
(log.f64 -1)
(-.f64 (log.f64 -1) (*.f64 2 (/.f64 1 eps)))
(-.f64 (log.f64 -1) (/.f64 2 eps))
(+.f64 (log.f64 -1) (/.f64 -2 eps))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))))
(-.f64 (log.f64 -1) (+.f64 (/.f64 2 eps) (/.f64 2/3 (pow.f64 eps 3))))
(+.f64 (-.f64 (log.f64 -1) (/.f64 2/3 (pow.f64 eps 3))) (/.f64 -2 eps))
(+.f64 (log.f64 -1) (+.f64 (/.f64 -2 eps) (/.f64 -2/3 (pow.f64 eps 3))))
(+.f64 (+.f64 (log.f64 -1) (/.f64 -2 eps)) (/.f64 -2/3 (pow.f64 eps 3)))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (+.f64 (.f64 2 (/.f64 1 eps)) (*.f64 2/5 (/.f64 1 (pow.f64 eps 5))))))
(-.f64 (log.f64 -1) (+.f64 (/.f64 2/3 (pow.f64 eps 3)) (+.f64 (/.f64 2 eps) (/.f64 2/5 (pow.f64 eps 5)))))
(-.f64 (-.f64 (log.f64 -1) (+.f64 (/.f64 2 eps) (/.f64 2/5 (pow.f64 eps 5)))) (/.f64 2/3 (pow.f64 eps 3)))
(+.f64 (log.f64 -1) (+.f64 (+.f64 (/.f64 -2 eps) (/.f64 -2/3 (pow.f64 eps 3))) (/.f64 -2/5 (pow.f64 eps 5))))
1
(+.f64 (*.f64 -2 eps) 1)
(fma.f64 -2 eps 1)
(+.f64 (.f64 -2 eps) (+.f64 (.f64 2 (pow.f64 eps 2)) 1))
(fma.f64 -2 eps (fma.f64 2 (*.f64 eps eps) 1))
(fma.f64 -2 eps (fma.f64 eps (*.f64 eps 2) 1))
(fma.f64 eps (fma.f64 eps 2 -2) 1)
(+.f64 (.f64 -2 eps) (+.f64 (.f64 2 (pow.f64 eps 2)) (+.f64 1 (*.f64 -2 (pow.f64 eps 3)))))
(fma.f64 -2 eps (+.f64 (fma.f64 2 (.f64 eps eps) 1) (.f64 -2 (pow.f64 eps 3))))
(fma.f64 -2 eps (fma.f64 2 (*.f64 eps eps) (fma.f64 -2 (pow.f64 eps 3) 1)))
(fma.f64 -2 eps (fma.f64 -2 (pow.f64 eps 3) (fma.f64 eps (*.f64 eps 2) 1)))
(fma.f64 -2 (pow.f64 eps 3) (fma.f64 eps (fma.f64 eps 2 -2) 1))
-1
(-.f64 (*.f64 2 (/.f64 1 eps)) 1)
(+.f64 (/.f64 2 eps) -1)
(+.f64 -1 (/.f64 2 eps))
(-.f64 (.f64 2 (/.f64 1 eps)) (+.f64 1 (.f64 2 (/.f64 1 (pow.f64 eps 2)))))
(-.f64 (/.f64 2 eps) (+.f64 1 (/.f64 2 (*.f64 eps eps))))
(+.f64 (/.f64 2 eps) (-.f64 -1 (/.f64 2 (*.f64 eps eps))))
(+.f64 -1 (+.f64 (/.f64 2 eps) (/.f64 -2 (*.f64 eps eps))))
(-.f64 (+.f64 (.f64 2 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 eps 2)))))
(+.f64 (/.f64 2 (pow.f64 eps 3)) (-.f64 (/.f64 2 eps) (+.f64 1 (/.f64 2 (*.f64 eps eps)))))
(+.f64 (/.f64 2 eps) (-.f64 (/.f64 2 (pow.f64 eps 3)) (+.f64 1 (/.f64 2 (*.f64 eps eps)))))
(+.f64 -1 (+.f64 (/.f64 -2 (*.f64 eps eps)) (+.f64 (/.f64 2 eps) (/.f64 2 (pow.f64 eps 3)))))
(+.f64 -1 (+.f64 (/.f64 2 eps) (*.f64 (/.f64 (/.f64 1 eps) eps) (+.f64 (/.f64 2 eps) -2))))
(+.f64 (/.f64 2 eps) (fma.f64 (/.f64 (/.f64 1 eps) eps) (+.f64 -2 (/.f64 2 eps)) -1))
-1
(-.f64 (*.f64 2 (/.f64 1 eps)) 1)
(+.f64 (/.f64 2 eps) -1)
(+.f64 -1 (/.f64 2 eps))
(-.f64 (.f64 2 (/.f64 1 eps)) (+.f64 1 (.f64 2 (/.f64 1 (pow.f64 eps 2)))))
(-.f64 (/.f64 2 eps) (+.f64 1 (/.f64 2 (*.f64 eps eps))))
(+.f64 (/.f64 2 eps) (-.f64 -1 (/.f64 2 (*.f64 eps eps))))
(+.f64 -1 (+.f64 (/.f64 2 eps) (/.f64 -2 (*.f64 eps eps))))
(-.f64 (+.f64 (.f64 2 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 eps 2)))))
(+.f64 (/.f64 2 (pow.f64 eps 3)) (-.f64 (/.f64 2 eps) (+.f64 1 (/.f64 2 (*.f64 eps eps)))))
(+.f64 (/.f64 2 eps) (-.f64 (/.f64 2 (pow.f64 eps 3)) (+.f64 1 (/.f64 2 (*.f64 eps eps)))))
(+.f64 -1 (+.f64 (/.f64 -2 (*.f64 eps eps)) (+.f64 (/.f64 2 eps) (/.f64 2 (pow.f64 eps 3)))))
(+.f64 -1 (+.f64 (/.f64 2 eps) (*.f64 (/.f64 (/.f64 1 eps) eps) (+.f64 (/.f64 2 eps) -2))))
(+.f64 (/.f64 2 eps) (fma.f64 (/.f64 (/.f64 1 eps) eps) (+.f64 -2 (/.f64 2 eps)) -1))
(*.f64 -2 eps)
(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
(fma.f64 -2 eps (*.f64 -2/3 (pow.f64 eps 3)))
(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
(+.f64 (.f64 -2 eps) (+.f64 (.f64 -2/5 (pow.f64 eps 5)) (*.f64 -2/3 (pow.f64 eps 3))))
(fma.f64 -2 eps (fma.f64 -2/5 (pow.f64 eps 5) (*.f64 -2/3 (pow.f64 eps 3))))
(fma.f64 -2 eps (fma.f64 -2/3 (pow.f64 eps 3) (*.f64 -2/5 (pow.f64 eps 5))))
(+.f64 (.f64 -2 eps) (+.f64 (.f64 -2/5 (pow.f64 eps 5)) (+.f64 (.f64 -2/7 (pow.f64 eps 7)) (.f64 -2/3 (pow.f64 eps 3)))))
(fma.f64 -2 eps (fma.f64 -2/5 (pow.f64 eps 5) (fma.f64 -2/7 (pow.f64 eps 7) (*.f64 -2/3 (pow.f64 eps 3)))))
(fma.f64 -2 eps (fma.f64 -2/5 (pow.f64 eps 5) (fma.f64 -2/3 (pow.f64 eps 3) (*.f64 -2/7 (pow.f64 eps 7)))))
(fma.f64 -2 eps (fma.f64 -2/3 (pow.f64 eps 3) (fma.f64 -2/5 (pow.f64 eps 5) (*.f64 -2/7 (pow.f64 eps 7)))))
(log.f64 -1)
(-.f64 (log.f64 -1) (*.f64 2 (/.f64 1 eps)))
(-.f64 (log.f64 -1) (/.f64 2 eps))
(+.f64 (log.f64 -1) (/.f64 -2 eps))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (.f64 2 (/.f64 1 eps))))
(-.f64 (log.f64 -1) (+.f64 (/.f64 2 eps) (/.f64 2/3 (pow.f64 eps 3))))
(+.f64 (-.f64 (log.f64 -1) (/.f64 2/3 (pow.f64 eps 3))) (/.f64 -2 eps))
(+.f64 (log.f64 -1) (+.f64 (/.f64 -2 eps) (/.f64 -2/3 (pow.f64 eps 3))))
(+.f64 (+.f64 (log.f64 -1) (/.f64 -2 eps)) (/.f64 -2/3 (pow.f64 eps 3)))
(-.f64 (log.f64 -1) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (+.f64 (.f64 2 (/.f64 1 eps)) (*.f64 2/5 (/.f64 1 (pow.f64 eps 5))))))
(-.f64 (log.f64 -1) (+.f64 (/.f64 2/3 (pow.f64 eps 3)) (+.f64 (/.f64 2 eps) (/.f64 2/5 (pow.f64 eps 5)))))
(-.f64 (-.f64 (log.f64 -1) (+.f64 (/.f64 2 eps) (/.f64 2/5 (pow.f64 eps 5)))) (/.f64 2/3 (pow.f64 eps 3)))
(+.f64 (log.f64 -1) (+.f64 (+.f64 (/.f64 -2 eps) (/.f64 -2/3 (pow.f64 eps 3))) (/.f64 -2/5 (pow.f64 eps 5))))
(*.f64 -1 (log.f64 -1))
(neg.f64 (log.f64 -1))
(-.f64 (.f64 -1 (log.f64 -1)) (.f64 2 (/.f64 1 eps)))
(-.f64 (neg.f64 (log.f64 -1)) (/.f64 2 eps))
(fma.f64 -1 (log.f64 -1) (/.f64 -2 eps))
(-.f64 (/.f64 -2 eps) (log.f64 -1))
(-.f64 (.f64 -1 (log.f64 -1)) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (*.f64 2 (/.f64 1 eps))))
(-.f64 (neg.f64 (log.f64 -1)) (+.f64 (/.f64 2 eps) (/.f64 2/3 (pow.f64 eps 3))))
(-.f64 (fma.f64 -1 (log.f64 -1) (/.f64 -2 eps)) (/.f64 2/3 (pow.f64 eps 3)))
(+.f64 (-.f64 (/.f64 -2 eps) (log.f64 -1)) (/.f64 -2/3 (pow.f64 eps 3)))
(-.f64 (.f64 -1 (log.f64 -1)) (+.f64 (.f64 2/3 (/.f64 1 (pow.f64 eps 3))) (+.f64 (.f64 2 (/.f64 1 eps)) (.f64 2/5 (/.f64 1 (pow.f64 eps 5))))))
(-.f64 (neg.f64 (log.f64 -1)) (+.f64 (/.f64 2/3 (pow.f64 eps 3)) (+.f64 (/.f64 2 eps) (/.f64 2/5 (pow.f64 eps 5)))))
(-.f64 (-.f64 (fma.f64 -1 (log.f64 -1) (/.f64 -2 eps)) (/.f64 2/3 (pow.f64 eps 3))) (/.f64 2/5 (pow.f64 eps 5)))
(-.f64 (+.f64 (+.f64 (/.f64 -2 eps) (/.f64 -2/3 (pow.f64 eps 3))) (/.f64 -2/5 (pow.f64 eps 5))) (log.f64 -1))
(+.f64 (+.f64 (-.f64 (/.f64 -2 eps) (log.f64 -1)) (/.f64 -2/3 (pow.f64 eps 3))) (/.f64 -2/5 (pow.f64 eps 5)))
0
1
0

eval66.0ms (1.2%)

Compiler: Compiled 820 to 660 computations (19.5% saved)

prune10.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	63	5	68

Accuracy

100.0%

Counts

68 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
▶	99.9%	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
▶	99.5%	(*.f64 -2 eps)
✓	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.5%	0
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
▶	99.9%	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
▶	99.5%	(*.f64 -2 eps)
✓	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.5%	0

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize47.0ms (0.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.5%	(*.f64 eps -2/3)

Compiler

Compiled 27 to 18 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	inf	(*.f64 eps -2/3)
0.0ms	eps	@	-inf	(*.f64 eps -2/3)
0.0ms	eps	@	0	(*.f64 eps -2/3)

rewrite45.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`pow1`
860×	`add-sqr-sqrt`
842×	`*-un-lft-identity`
816×	`add-exp-log`
816×	`log1p-expm1-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	100	7
2	1111	7

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

Inputs
(*.f64 eps -2/3)

Outputs
(+.f64 0 (*.f64 eps -2/3))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps)) (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -2/3) eps))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -2/3) eps))))
(-.f64 (+.f64 1 (*.f64 eps -2/3)) 1)
(pow.f64 (*.f64 eps -2/3) 1)
(pow.f64 (cbrt.f64 (*.f64 eps -2/3)) 3)
(pow.f64 (pow.f64 (*.f64 eps -2/3) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 eps -2/3)) 2)
(sqrt.f64 (.f64 (.f64 eps eps) 4/9))
(log.f64 (pow.f64 (exp.f64 -2/3) eps))
(cbrt.f64 (pow.f64 (*.f64 eps -2/3) 3))
(expm1.f64 (log1p.f64 (*.f64 eps -2/3)))
(exp.f64 (log.f64 (*.f64 eps -2/3)))
(log1p.f64 (expm1.f64 (*.f64 eps -2/3)))

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1582×	`log-prod`
1574×	`fma-def`
1110×	`fma-neg`
518×	`associate-r`
512×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	238
1	94	224
2	309	200
3	2201	200
4	4992	200
5	7216	200

Stop Event

1×	node limit

Counts

26 → 18

Calls

Call 1

Inputs
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(+.f64 0 (*.f64 eps -2/3))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps)) (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -2/3) eps))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -2/3) eps))))
(-.f64 (+.f64 1 (*.f64 eps -2/3)) 1)
(pow.f64 (*.f64 eps -2/3) 1)
(pow.f64 (cbrt.f64 (*.f64 eps -2/3)) 3)
(pow.f64 (pow.f64 (*.f64 eps -2/3) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 eps -2/3)) 2)
(sqrt.f64 (.f64 (.f64 eps eps) 4/9))
(log.f64 (pow.f64 (exp.f64 -2/3) eps))
(cbrt.f64 (pow.f64 (*.f64 eps -2/3) 3))
(expm1.f64 (log1p.f64 (*.f64 eps -2/3)))
(exp.f64 (log.f64 (*.f64 eps -2/3)))
(log1p.f64 (expm1.f64 (*.f64 eps -2/3)))

Outputs
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(*.f64 -2/3 eps)
(+.f64 0 (*.f64 eps -2/3))
(*.f64 -2/3 eps)
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps)) (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps))))
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -2/3) eps))) 3)
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -2/3) eps))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -2/3) eps))))
(*.f64 -2/3 eps)
(-.f64 (+.f64 1 (*.f64 eps -2/3)) 1)
(*.f64 -2/3 eps)
(pow.f64 (*.f64 eps -2/3) 1)
(*.f64 -2/3 eps)
(pow.f64 (cbrt.f64 (*.f64 eps -2/3)) 3)
(*.f64 -2/3 eps)
(pow.f64 (pow.f64 (*.f64 eps -2/3) 3) 1/3)
(*.f64 -2/3 eps)
(pow.f64 (sqrt.f64 (*.f64 eps -2/3)) 2)
(*.f64 -2/3 eps)
(sqrt.f64 (.f64 (.f64 eps eps) 4/9))
(*.f64 -2/3 eps)
(log.f64 (pow.f64 (exp.f64 -2/3) eps))
(*.f64 -2/3 eps)
(cbrt.f64 (pow.f64 (*.f64 eps -2/3) 3))
(*.f64 -2/3 eps)
(expm1.f64 (log1p.f64 (*.f64 eps -2/3)))
(*.f64 -2/3 eps)
(exp.f64 (log.f64 (*.f64 eps -2/3)))
(*.f64 -2/3 eps)
(log1p.f64 (expm1.f64 (*.f64 eps -2/3)))
(*.f64 -2/3 eps)

eval5.0ms (0.1%)

Compiler: Compiled 225 to 166 computations (26.2% saved)

prune5.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	18	0	18
Fresh	0	1	1
Picked	0	2	2
Done	0	2	2
Total	18	5	23

Accuracy

100.0%

Counts

23 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	99.9%	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
✓	99.5%	(*.f64 -2 eps)
✓	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.5%	0
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	99.9%	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
✓	99.5%	(*.f64 -2 eps)
✓	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.5%	0

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune4.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	99.9%	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
✓	99.5%	(*.f64 -2 eps)
✓	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.5%	0
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	99.9%	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
✓	99.5%	(*.f64 -2 eps)
✓	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.5%	0

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	99.9%	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
✓	99.5%	(*.f64 -2 eps)
✓	7.7%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.5%	0

Compiler

Compiled 58 to 42 computations (27.6% saved)

regimes11.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

Inputs
0
(*.f64 -2 eps)
(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))

Outputs
(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))

Calls

3 calls:

4.0ms	eps
3.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
2.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Results

Accuracy	Segments	Branch
100.0%	1	`eps`
100.0%	1	`(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))`
100.0%	1	`(/.f64 (-.f64 1 eps) (+.f64 1 eps))`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes9.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
0
(*.f64 -2 eps)
(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))

Outputs
(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))

Calls

3 calls:

4.0ms	eps
2.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
2.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))

Results

Accuracy	Segments	Branch
99.9%	1	`eps`
99.9%	1	`(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))`
99.9%	1	`(/.f64 (-.f64 1 eps) (+.f64 1 eps))`

Compiler

Compiled 40 to 29 computations (27.5% saved)

regimes8.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
0
(*.f64 -2 eps)
(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Outputs
(*.f64 -2 eps)

Calls

3 calls:

4.0ms	eps
2.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
2.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))

Results

Accuracy	Segments	Branch
99.5%	1	`eps`
99.5%	1	`(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))`
99.5%	1	`(/.f64 (-.f64 1 eps) (+.f64 1 eps))`

Compiler

Compiled 32 to 24 computations (25% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
0

Outputs
0

Calls

1 calls:

3.0ms

eps

Results

Accuracy	Segments	Branch
5.5%	1	`eps`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative`
6×	`sub-neg`
6×	`+-commutative`
4×	`neg-mul-1`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	48
1	24	48
2	29	48
3	32	48
4	33	48

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
(*.f64 -2 eps)
0

Outputs
(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
(*.f64 -2 eps)
(*.f64 eps -2)
0

Compiler

Compiled 22 to 16 computations (27.3% saved)

soundness841.0ms (16%)

Rules

8722×	`fma-def`
1534×	`prod-diff`
1482×	`fma-def`
1230×	`fma-neg`
1220×	`unsub-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	73
1	37	57
2	70	57
3	148	57
4	377	57
5	984	57
6	1861	57
7	2532	57
8	3523	57
9	4766	57
10	5322	57
11	5483	57
12	5658	57
13	6107	57
14	7004	57
15	7072	57
16	7104	57
17	7124	57
18	7216	57
19	7357	57
20	7477	57
21	7477	57
0	13	57
1	279	49
2	3805	3
0	64	945
1	182	935
2	460	929
3	1293	917
4	3996	909

Stop Event

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

Compiler

Compiled 277 to 204 computations (26.4% saved)

end0.0ms (0%)

preprocess52.0ms (1%)

Compiler: Compiled 88 to 66 computations (25% saved)

analyze3.0ms (0.1%)

sample3.4s (64.5%)

preprocess312.0ms (5.9%)

eval0.0ms (0%)

prune2.0ms (0%)

localize202.0ms (3.8%)

series4.0ms (0.1%)

rewrite62.0ms (1.2%)

simplify61.0ms (1.2%)

eval66.0ms (1.2%)

prune10.0ms (0.2%)

localize47.0ms (0.9%)

series1.0ms (0%)

rewrite45.0ms (0.9%)

simplify64.0ms (1.2%)

eval5.0ms (0.1%)

prune5.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune4.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes11.0ms (0.2%)

regimes9.0ms (0.2%)

regimes8.0ms (0.2%)

regimes3.0ms (0.1%)

simplify46.0ms (0.9%)

soundness841.0ms (16%)

end0.0ms (0%)

preprocess52.0ms (1%)

Profiling