Metrics for logq (problem 3.4.3)

analyze1.2s (12.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	199.9%	-99.9%	0%	0%	0%	1
0%	0%	399.8%	-299.8%	0%	0%	0%	2
0%	0%	799.6%	-699.6%	0%	0%	0%	3
0%	0%	1599.2%	-1499.2%	0%	0%	0%	4
0%	0%	3198.4%	-3098.4%	0%	0%	0%	5
0%	0%	6396.9%	-6296.9%	0%	0%	0%	6
0%	0%	12793.8%	-12693.8%	0%	0%	0%	7
0%	0%	25587.5%	-25487.5%	0%	0%	0%	8
0%	0%	51175%	-51075%	0%	0%	0%	9
0%	0%	102350%	-102250%	0%	0%	0%	10
0%	0%	204700%	-204600%	0%	0%	0%	11
0%	0%	409400%	-409300%	0%	0%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample5.8s (61.8%)

Results

1.9s	2782×	body	4096	valid
1.5s	2798×	body	2048	valid
1.3s	8281×	body	256	invalid
694.0ms	1329×	body	1024	valid
163.0ms	657×	body	512	valid
109.0ms	690×	body	256	valid

Bogosity

preprocess462.0ms (4.9%)

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	50
1	37	38
2	70	38
3	148	38
4	377	38
5	984	38
6	1861	38
7	2532	38
8	3523	38
9	4766	38
10	5322	38
11	5483	38
12	5658	38
13	6107	38
14	7004	38
15	7072	38
16	7104	38
17	7124	38
18	7216	38
19	7357	38
20	7477	38
21	7477	38

Stop Event

1×	node limit

Calls

Call 1

Inputs
(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 (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 10 to 8 computations (20% saved)

simplify285.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

3044×	`fma-def`
1338×	`distribute-lft-in`
944×	`fma-neg`
932×	`sub-neg`
644×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	20	19
2	30	19
3	44	19
4	74	19
5	106	19
6	163	19
7	296	19
8	602	19
9	1053	19
10	1462	19
11	2037	19
12	2865	19
13	4066	19
14	4900	19
15	4996	19
16	5028	19
17	5028	19
18	6533	19
19	7165	19
20	7243	19
21	7251	19
22	7259	19
23	7259	19
24	7459	19

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Accurracy

100.0%

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
▶	8.4%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
▶	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
▶	8.4%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 32 to 24 computations (25% saved)

localize338.0ms (3.6%)

Local Accuracy

Found 4 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(log1p.f64 (neg.f64 eps))
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	100.0%	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
✓	8.5%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 39 to 22 computations (43.6% saved)

series4.0ms (0%)

Counts

4 → 48

Calls

12 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)))

rewrite80.0ms (0.9%)

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	66
1	279	54
2	3805	8

Stop Event

1×	node limit

Counts

4 → 49

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))
(log1p.f64 (neg.f64 eps))

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

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

828×	`associate-+r+`
812×	`cancel-sign-sub-inv`
808×	`associate-+l+`
548×	`associate--r+`
516×	`distribute-lft-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	2107
1	524	1977
2	2031	1963

Stop Event

1×	node limit

Counts

97 → 157

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

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)))
(fma.f64 -2/3 (pow.f64 eps 3) (*.f64 -2 eps))
(+.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))))
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(*.f64 (log1p.f64 eps) 1)
(log1p.f64 eps)
(*.f64 (cbrt.f64 (log1p.f64 eps)) (pow.f64 (cbrt.f64 (log1p.f64 eps)) 2))
(log1p.f64 eps)
(*.f64 (pow.f64 (cbrt.f64 (log1p.f64 eps)) 2) (cbrt.f64 (log1p.f64 eps)))
(log1p.f64 eps)
(*.f64 (sqrt.f64 (log1p.f64 eps)) (sqrt.f64 (log1p.f64 eps)))
(log1p.f64 eps)
(.f64 3 (.f64 1/3 (log1p.f64 eps)))
(log1p.f64 eps)
(.f64 2 (.f64 1/2 (log1p.f64 eps)))
(log1p.f64 eps)
(.f64 1/3 (.f64 3 (log1p.f64 eps)))
(log1p.f64 eps)
(pow.f64 (log1p.f64 eps) 1)
(log1p.f64 eps)
(pow.f64 (cbrt.f64 (log1p.f64 eps)) 3)
(log1p.f64 eps)
(pow.f64 (pow.f64 (log1p.f64 eps) 3) 1/3)
(log1p.f64 eps)
(pow.f64 (sqrt.f64 (log1p.f64 eps)) 2)
(log1p.f64 eps)
(neg.f64 (log.f64 (/.f64 (+.f64 1 eps) (+.f64 1 (*.f64 eps eps)))))
(-.f64 (log1p.f64 (*.f64 eps eps)) (log1p.f64 eps))
(neg.f64 (log.f64 (/.f64 (+.f64 1 (fma.f64 eps eps eps)) (+.f64 1 (pow.f64 eps 3)))))
(+.f64 (log1p.f64 (pow.f64 eps 3)) (neg.f64 (log.f64 (+.f64 1 (fma.f64 eps eps eps)))))
(-.f64 (log1p.f64 (pow.f64 eps 3)) (log1p.f64 (fma.f64 eps eps eps)))
(sqrt.f64 (pow.f64 (log1p.f64 eps) 2))
(log1p.f64 eps)
(log.f64 (+.f64 1 eps))
(log1p.f64 eps)
(cbrt.f64 (pow.f64 (log1p.f64 eps) 3))
(log1p.f64 eps)
(expm1.f64 (log1p.f64 (log1p.f64 eps)))
(log1p.f64 eps)
(exp.f64 (log.f64 (log1p.f64 eps)))
(log1p.f64 eps)
(exp.f64 (*.f64 (log.f64 (log1p.f64 eps)) 1))
(log1p.f64 eps)
(exp.f64 (.f64 (.f64 (log.f64 (log1p.f64 eps)) 1) 1))
(log1p.f64 eps)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (log1p.f64 eps))) 3))
(log1p.f64 eps)
(exp.f64 (.f64 (.f64 3 (log.f64 (log1p.f64 eps))) 1/3))
(log1p.f64 eps)
(exp.f64 (.f64 (.f64 (log.f64 (log1p.f64 eps)) 3) 1/3))
(log1p.f64 eps)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (log1p.f64 eps))) 2))
(log1p.f64 eps)

eval41.0ms (0.4%)

Compiler: Compiled 2127 to 1398 computations (34.3% saved)

prune33.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	154	5	159

Accurracy

100.0%

Counts

159 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
▶	99.3%	(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
▶	98.8%	(*.f64 -2 eps)
✓	8.4%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.3%	0
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
▶	99.3%	(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
▶	98.8%	(*.f64 -2 eps)
✓	8.4%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.3%	0

Compiler

Compiled 64 to 50 computations (21.9% saved)

localize151.0ms (1.6%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.8%	(*.f64 -2/3 (pow.f64 eps 3))

Compiler

Compiled 31 to 23 computations (25.8% saved)

series2.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(*.f64 -2/3 (pow.f64 eps 3))
1.0ms	eps	@	0	(*.f64 -2/3 (pow.f64 eps 3))
0.0ms	eps	@	-inf	(*.f64 -2/3 (pow.f64 eps 3))

rewrite54.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1204×	`pow1`
1126×	`add-exp-log`
1126×	`log1p-expm1-u`
1126×	`expm1-log1p-u`
1102×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	149	13
2	1572	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(*.f64 -2/3 (pow.f64 eps 3))

Outputs
(-.f64 (+.f64 1 (*.f64 -2/3 (pow.f64 eps 3))) 1)
(pow.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1)
(pow.f64 (*.f64 eps (cbrt.f64 -2/3)) 3)
(pow.f64 (pow.f64 (*.f64 -2/3 (pow.f64 eps 3)) 3) 1/3)
(pow.f64 (*.f64 (sqrt.f64 -2/3) (pow.f64 eps 3/2)) 2)
(sqrt.f64 (*.f64 (pow.f64 eps 6) 4/9))
(log.f64 (pow.f64 (exp.f64 -2/3) (pow.f64 eps 3)))
(cbrt.f64 (pow.f64 (*.f64 -2/3 (pow.f64 eps 3)) 3))
(expm1.f64 (log1p.f64 (*.f64 -2/3 (pow.f64 eps 3))))
(exp.f64 (log.f64 (*.f64 -2/3 (pow.f64 eps 3))))
(log1p.f64 (expm1.f64 (*.f64 -2/3 (pow.f64 eps 3))))

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

2268×	`log-prod`
918×	`exp-sum`
820×	`distribute-rgt-in`
818×	`distribute-lft-in`
650×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	275
1	98	209
2	313	143
3	1886	143
4	6007	143

Stop Event

1×	node limit

Counts

11 → 14

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (*.f64 -2/3 (pow.f64 eps 3))) 1)
(pow.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1)
(pow.f64 (*.f64 eps (cbrt.f64 -2/3)) 3)
(pow.f64 (pow.f64 (*.f64 -2/3 (pow.f64 eps 3)) 3) 1/3)
(pow.f64 (*.f64 (sqrt.f64 -2/3) (pow.f64 eps 3/2)) 2)
(sqrt.f64 (*.f64 (pow.f64 eps 6) 4/9))
(log.f64 (pow.f64 (exp.f64 -2/3) (pow.f64 eps 3)))
(cbrt.f64 (pow.f64 (*.f64 -2/3 (pow.f64 eps 3)) 3))
(expm1.f64 (log1p.f64 (*.f64 -2/3 (pow.f64 eps 3))))
(exp.f64 (log.f64 (*.f64 -2/3 (pow.f64 eps 3))))
(log1p.f64 (expm1.f64 (*.f64 -2/3 (pow.f64 eps 3))))

Outputs
(-.f64 (+.f64 1 (*.f64 -2/3 (pow.f64 eps 3))) 1)
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(pow.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1)
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(pow.f64 (*.f64 eps (cbrt.f64 -2/3)) 3)
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(pow.f64 (pow.f64 (*.f64 -2/3 (pow.f64 eps 3)) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(pow.f64 (*.f64 (sqrt.f64 -2/3) (pow.f64 eps 3/2)) 2)
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(sqrt.f64 (*.f64 (pow.f64 eps 6) 4/9))
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(log.f64 (pow.f64 (exp.f64 -2/3) (pow.f64 eps 3)))
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(cbrt.f64 (pow.f64 (*.f64 -2/3 (pow.f64 eps 3)) 3))
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(expm1.f64 (log1p.f64 (*.f64 -2/3 (pow.f64 eps 3))))
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(exp.f64 (log.f64 (*.f64 -2/3 (pow.f64 eps 3))))
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))
(log1p.f64 (expm1.f64 (*.f64 -2/3 (pow.f64 eps 3))))
(+.f64 1 (-.f64 (*.f64 -2/3 (pow.f64 eps 3)) 1))
(+.f64 (*.f64 -2/3 (pow.f64 eps 3)) 0)
(*.f64 -2/3 (pow.f64 eps 3))

eval4.0ms (0%)

Compiler: Compiled 159 to 131 computations (17.6% saved)

prune5.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	1	1
Picked	0	2	2
Done	0	2	2
Total	14	5	19

Accurracy

100.0%

Counts

19 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	99.3%	(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
✓	98.8%	(*.f64 -2 eps)
✓	8.4%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.3%	0
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	99.3%	(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
✓	98.8%	(*.f64 -2 eps)
✓	8.4%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.3%	0

Compiler

Compiled 64 to 50 computations (21.9% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune4.0ms (0%)

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

Accurracy

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))
✓	99.3%	(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
✓	98.8%	(*.f64 -2 eps)
✓	8.4%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.3%	0
✓	100.0%	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	99.3%	(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
✓	98.8%	(*.f64 -2 eps)
✓	8.4%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.3%	0

Compiler

Compiled 64 to 50 computations (21.9% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune5.0ms (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

Accurracy

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))
✓	99.3%	(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
✓	98.8%	(*.f64 -2 eps)
✓	8.4%	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	5.3%	0

Compiler

Compiled 60 to 46 computations (23.3% saved)

regimes10.0ms (0.1%)

Counts

5 → 1

Calls

Call 1

Inputs
0
(*.f64 -2 eps)
(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))
(-.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
2.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
2.0ms	(/.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 47 to 35 computations (25.5% saved)

regimes11.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(+.f64 (.f64 -2 eps) (.f64 -2/3 (pow.f64 eps 3)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`eps`
99.3%	1	`(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))`
99.3%	1	`(/.f64 (-.f64 1 eps) (+.f64 1 eps))`

Compiler

Compiled 41 to 31 computations (24.4% saved)

regimes9.0ms (0.1%)

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:

3.0ms	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
98.8%	1	`eps`
98.8%	1	`(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))`
98.8%	1	`(/.f64 (-.f64 1 eps) (+.f64 1 eps))`

Compiler

Compiled 32 to 24 computations (25% saved)

regimes8.0ms (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:

5.0ms

eps

Results

Accuracy	Segments	Branch
5.3%	1	`eps`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	24	52
2	29	52
3	32	52
4	33	52

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 23 to 18 computations (21.7% saved)

soundness652.0ms (7%)

Rules

3044×	`fma-def`
1534×	`prod-diff`
1338×	`distribute-lft-in`
944×	`fma-neg`
932×	`sub-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	20	19
2	30	19
3	44	19
4	74	19
5	106	19
6	163	19
7	296	19
8	602	19
9	1053	19
10	1462	19
11	2037	19
12	2865	19
13	4066	19
14	4900	19
15	4996	19
16	5028	19
17	5028	19
18	6533	19
19	7165	19
20	7243	19
21	7251	19
22	7259	19
23	7259	19
24	7459	19
0	13	66
1	279	54
2	3805	8

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 181 to 136 computations (24.9% saved)

end0.0ms (0%)

preprocess50.0ms (0.5%)

Compiler: Compiled 90 to 70 computations (22.2% saved)

analyze1.2s (12.7%)

sample5.8s (61.8%)

preprocess462.0ms (4.9%)

simplify285.0ms (3.1%)

eval1.0ms (0%)

prune2.0ms (0%)

localize338.0ms (3.6%)

series4.0ms (0%)

rewrite80.0ms (0.9%)

simplify78.0ms (0.8%)

eval41.0ms (0.4%)

prune33.0ms (0.4%)

localize151.0ms (1.6%)

series2.0ms (0%)

rewrite54.0ms (0.6%)

simplify90.0ms (1%)

eval4.0ms (0%)

prune5.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune4.0ms (0%)

localize0.0ms (0%)

eval0.0ms (0%)

prune5.0ms (0.1%)

regimes10.0ms (0.1%)

regimes11.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

simplify6.0ms (0.1%)

soundness652.0ms (7%)

end0.0ms (0%)

preprocess50.0ms (0.5%)

Profiling