Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.9s (27.8%)

Results

977.0ms	2337×	body	1024	valid
465.0ms	4378×	body	128	valid
290.0ms	1016×	body	512	valid
96.0ms	525×	body	256	valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

235×	`fma-neg_binary64`
124×	`rules-11_binary64`
121×	`rules-40_binary64`
121×	`rules-41_binary64`
121×	`rules-42_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	56	17
2	164	17
3	520	17
4	119	17

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

21.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.2b	(/.f64 1 (sqrt.f64 x))
✓	3.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series38.0ms (0.6%)

Counts

3 → 4

Calls

3 calls:

15.0ms	(/.f64 1 (sqrt.f64 x))
14.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite101.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

826×	`fma-neg_binary64`
607×	`prod-diff_binary64`
161×	`expm1-udef_binary64`
161×	`log1p-udef_binary64`
132×	`egg-rr`

Counts

3 → 132

Calls

3 calls:

98.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
98.0ms	(/.f64 1 (sqrt.f64 x))
98.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	217	24
2	2726	24
3	4939	24
4	4913	24
0	0	0
1	0	0

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1014×	`rules-43_binary64`
556×	`rules-40_binary64`
556×	`rules-41_binary64`
556×	`rules-42_binary64`
434×	`rules-15-rev_binary64`

Counts

136 → 136

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	4
1	119	4
2	414	4
3	2010	4
4	4665	4
5	33	4

prune182.0ms (2.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	122	14	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	14	137

Error

20.5b

Counts

137 → 14

Alt Table

Status	Error	Program
	32.2b	(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
	30.6b	(+.f64 (fma.f64 1 (pow.f64 x -1/2) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
	31.2b	(fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	30.7b	(/.f64 (/.f64 (fma.f64 (pow.f64 x -1/2) (sqrt.f64 (+.f64 1 x)) -1) (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
	30.7b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	30.9b	(fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	23.2b	(/.f64 (/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (pow.f64 x 1/4)) (pow.f64 x 1/4))
	30.5b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
	30.3b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
	31.3b	(fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	30.7b	(/.f64 (fma.f64 (pow.f64 x -1/2) (sqrt.f64 (+.f64 1 x)) -1) (sqrt.f64 (+.f64 1 x)))
▶	21.2b	(*.f64 (-.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (+.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
	31.0b	(+.f64 (fma.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
	30.8b	(+.f64 (fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))

Compiler

Compiled 3288 to 2658 computations (19.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)
✓	0.1b	(pow.f64 (sqrt.f64 x) -1/2)
✓	0.2b	(*.f64 (-.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (+.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
✓	3.0b	(-.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2))

series164.0ms (2.4%)

Counts

4 → 4

Calls

4 calls:

85.0ms	(*.f64 (-.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (+.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
47.0ms	(-.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2))
17.0ms	(pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)
14.0ms	(pow.f64 (sqrt.f64 x) -1/2)

rewrite84.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

582×	`log-prod_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
210×	`log-pow_binary64`
190×	`log-div_binary64`

Counts

4 → 157

Calls

4 calls:

81.0ms	(pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)
81.0ms	(pow.f64 (sqrt.f64 x) -1/2)
81.0ms	(*.f64 (-.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (+.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
81.0ms	(-.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	52
1	295	37
2	3622	37
3	5647	37
0	0	0
1	0	0

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1014×	`rules-43_binary64`
556×	`rules-40_binary64`
556×	`rules-41_binary64`
556×	`rules-42_binary64`
434×	`rules-15-rev_binary64`

Counts

161 → 161

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	4
1	119	4
2	415	4
3	2015	4
4	4670	4
5	34	4

prune381.0ms (5.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	220	9	229
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	224	19	243

Error

20.4b

Counts

243 → 19

Alt Table

Status	Error	Program
	21.3b	(.f64 (.f64 (-.f64 (pow.f64 x -1/8) (pow.f64 (+.f64 x 1) -1/8)) (+.f64 (pow.f64 x -1/8) (pow.f64 (+.f64 x 1) -1/8))) (+.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
	30.3b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
	31.2b	(fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	30.7b	(/.f64 (/.f64 (fma.f64 (pow.f64 x -1/2) (sqrt.f64 (+.f64 1 x)) -1) (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
	23.2b	(/.f64 (/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (pow.f64 x 1/4)) (pow.f64 x 1/4))
	30.5b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
	31.3b	(fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	30.8b	(*.f64 (+.f64 (-.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/8)) (pow.f64 (+.f64 x 1) -1/8) (pow.f64 (+.f64 x 1) -1/4))) (+.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
	30.7b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/2)))
	30.7b	(/.f64 (fma.f64 (pow.f64 x -1/2) (sqrt.f64 (+.f64 1 x)) -1) (sqrt.f64 (+.f64 1 x)))
	30.7b	(*.f64 (+.f64 (-.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4)) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/4))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 (+.f64 x 1) -1/4))) (+.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
▶	21.2b	(/.f64 (-.f64 (pow.f64 x -3/4) (pow.f64 (+.f64 x 1) -3/4)) (/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4))))
	30.8b	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))
	31.1b	(*.f64 (fma.f64 (pow.f64 x -1/8) (pow.f64 x -1/8) (neg.f64 (pow.f64 (+.f64 x 1) -1/4))) (+.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
	30.6b	(+.f64 (fma.f64 1 (pow.f64 x -1/2) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
	31.4b	(*.f64 (fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (pow.f64 x -1/4)) (neg.f64 (pow.f64 (+.f64 x 1) -1/4))) (+.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
	50.8b	(.f64 (-.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/4))) (cbrt.f64 (exp.f64 (pow.f64 x -1/4))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/4))))) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
	31.0b	(+.f64 (fma.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
	30.8b	(+.f64 (fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))

Compiler

Compiled 7351 to 5826 computations (20.7% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 (pow.f64 x -3/4) (pow.f64 (+.f64 x 1) -3/4)) (/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4))))
✓	0.4b	(/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4)))
✓	2.9b	(-.f64 (pow.f64 x -3/4) (pow.f64 (+.f64 x 1) -3/4))
✓	15.3b	(pow.f64 (*.f64 x (+.f64 x 1)) -1/4)

series321.0ms (4.8%)

Counts

4 → 48

Calls

4 calls:

259.0ms	(/.f64 (-.f64 (pow.f64 x -3/4) (pow.f64 (+.f64 x 1) -3/4)) (/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4))))
49.0ms	(/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4)))
8.0ms	(-.f64 (pow.f64 x -3/4) (pow.f64 (+.f64 x 1) -3/4))
5.0ms	(pow.f64 (*.f64 x (+.f64 x 1)) -1/4)

rewrite93.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

284×	`prod-diff_binary64`
223×	`log1p-expm1-u_binary64`
223×	`expm1-log1p-u_binary64`
210×	`add-sqr-sqrt_binary64`
203×	`add-cbrt-cube_binary64`

Counts

4 → 152

Calls

4 calls:

89.0ms	(/.f64 (-.f64 (pow.f64 x -3/4) (pow.f64 (+.f64 x 1) -3/4)) (/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4))))
89.0ms	(/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4)))
89.0ms	(-.f64 (pow.f64 x -3/4) (pow.f64 (+.f64 x 1) -3/4))
89.0ms	(pow.f64 (*.f64 x (+.f64 x 1)) -1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	118
1	526	112
2	4663	112
3	5067	112
0	0	0
1	0	0

simplify150.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

681×	`rules-40_binary64`
681×	`rules-41_binary64`
681×	`rules-42_binary64`
681×	`rules-43_binary64`
270×	`rules-20_binary64`

Counts

200 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	759	9743
1	4799	9720
2	4978	9720

prune585.0ms (8.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	232	4	236
Fresh	16	2	18
Picked	1	0	1
Done	0	0	0
Total	249	6	255

Error

5.7b

Counts

255 → 6

Alt Table

Status	Error	Program
	30.7b	(/.f64 (/.f64 (fma.f64 (pow.f64 x -1/2) (sqrt.f64 (+.f64 1 x)) -1) (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
	48.6b	(/.f64 (-.f64 (fma.f64 3/4 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (.f64 77/128 (pow.f64 (/.f64 1 (pow.f64 x 15)) 1/4))) (.f64 21/32 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4))) (/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4))))
	48.8b	(/.f64 (-.f64 (fma.f64 3/4 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (.f64 77/128 (pow.f64 (/.f64 1 (pow.f64 x 15)) 1/4))) (fma.f64 1155/2048 (pow.f64 (/.f64 1 (pow.f64 x 19)) 1/4) (.f64 21/32 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)))) (/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4))))
	36.8b	(-.f64 (fma.f64 9/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (/.f64 1 (pow.f64 (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x))) 2))) (.f64 3/2 (/.f64 1 (.f64 (.f64 x x) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x))))))) (.f64 3/2 (/.f64 1 (.f64 (pow.f64 x 3) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x)))))))
▶	30.7b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/2)))
	36.1b	(/.f64 3/2 (.f64 (.f64 x x) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x)))))

Compiler

Compiled 22460 to 18443 computations (17.9% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x 1) -1/2)
✓	3.0b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
✓	33.0b	(fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/2))

series288.0ms (4.3%)

Counts

3 → 36

Calls

3 calls:

276.0ms	(fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/2))
7.0ms	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
4.0ms	(pow.f64 (+.f64 x 1) -1/2)

rewrite90.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

626×	`prod-diff_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
196×	`egg-rr`
119×	`add-sqr-sqrt_binary64`

Counts

3 → 196

Calls

3 calls:

84.0ms	(pow.f64 (+.f64 x 1) -1/2)
84.0ms	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
84.0ms	(fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	288	45
2	3293	45
3	5004	45
0	0	0
1	0	0

simplify107.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

589×	`rules-20_binary64`
429×	`rules-21_binary64`
307×	`rules-7-rev_binary64`
290×	`fma-neg_binary64`
189×	`rules-41_binary64`

Counts

232 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1275
1	789	1245
2	3727	902
3	4952	761
4	4986	761
5	4881	761

prune520.0ms (7.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	315	1	316
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	315	7	322

Error

3.2b

Counts

322 → 7

Alt Table

Status	Error	Program
	30.7b	(/.f64 (/.f64 (fma.f64 (pow.f64 x -1/2) (sqrt.f64 (+.f64 1 x)) -1) (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
	48.6b	(/.f64 (-.f64 (fma.f64 3/4 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (.f64 77/128 (pow.f64 (/.f64 1 (pow.f64 x 15)) 1/4))) (.f64 21/32 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4))) (/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4))))
	48.8b	(/.f64 (-.f64 (fma.f64 3/4 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (.f64 77/128 (pow.f64 (/.f64 1 (pow.f64 x 15)) 1/4))) (fma.f64 1155/2048 (pow.f64 (/.f64 1 (pow.f64 x 19)) 1/4) (.f64 21/32 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)))) (/.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (*.f64 x (+.f64 x 1)) -1/4))) (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4))))
	47.4b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 x -1/4) 2) x) (fma.f64 3/8 (/.f64 (pow.f64 x -1/2) (.f64 x x)) (.f64 5/16 (/.f64 (pow.f64 (pow.f64 x -1/4) 2) (pow.f64 x 3))))) (-.f64 (fma.f64 5/16 (/.f64 (pow.f64 x -1/2) (pow.f64 x 3)) (fma.f64 3/8 (/.f64 (pow.f64 (pow.f64 x -1/4) 2) (.f64 x x)) (pow.f64 (pow.f64 x -1/4) 2))) (.f64 (/.f64 (pow.f64 x -1/2) x) (-.f64 x 1/2)))))
	36.8b	(-.f64 (fma.f64 9/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (/.f64 1 (pow.f64 (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x))) 2))) (.f64 3/2 (/.f64 1 (.f64 (.f64 x x) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x))))))) (.f64 3/2 (/.f64 1 (.f64 (pow.f64 x 3) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x)))))))
✓	30.7b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/2)))
	36.1b	(/.f64 3/2 (.f64 (.f64 x x) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x)))))

Compiler

Compiled 14885 to 12322 computations (17.2% saved)

regimes1.0s (15.6%)

Accuracy

Total 0.4b remaining (13.6%)

Threshold costs 0.4b (13.6%)

Counts

261 → 4

Compiler

Compiled 12162 to 10078 computations (17.1% saved)

bsearch162.0ms (2.4%)

Steps

Iters	Range		Point
9	7.158177218003274e+200	6.1890418135198e+205	3.3300363174486925e+201
1	4.5661916787653195e+153	2.927160551598592e+154	1.1577094350749208e+154
8	191319.399765773	411065252.263275	386923.8565851494

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	251
1	72	251
2	71	251

end323.0ms (4.8%)

Compiler: Compiled 664 to 529 computations (20.3% saved)

Details

analyze1.0ms (0%)

sample1.9s (27.8%)

simplify18.0ms (0.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series38.0ms (0.6%)

rewrite101.0ms (1.5%)

simplify71.0ms (1%)

prune182.0ms (2.7%)

localize13.0ms (0.2%)

series164.0ms (2.4%)

rewrite84.0ms (1.2%)

simplify68.0ms (1%)

prune381.0ms (5.7%)

localize29.0ms (0.4%)

series321.0ms (4.8%)

rewrite93.0ms (1.4%)

simplify150.0ms (2.2%)

prune585.0ms (8.7%)

localize14.0ms (0.2%)

series288.0ms (4.3%)

rewrite90.0ms (1.3%)

simplify107.0ms (1.6%)

prune520.0ms (7.7%)

regimes1.0s (15.6%)

bsearch162.0ms (2.4%)

simplify4.0ms (0.1%)

end323.0ms (4.8%)

Profiling