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)

sample1.7s (37.3%)

Results

801.0ms	2322×	body	1024	valid
451.0ms	4334×	body	128	valid
278.0ms	1068×	body	512	valid
95.0ms	532×	body	256	valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17

Stop Event

1×

saturated

Counts

1 → 2

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

23.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	23.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	2.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series31.0ms (0.7%)

Counts

4 → 8

Calls

4 calls:

9.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(/.f64 1 (sqrt.f64 x))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(sqrt.f64 (+.f64 x 1))

rewrite58.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`prod-diff_binary64`
205×	`fma-neg_binary64`
170×	`log1p-udef_binary64`
169×	`expm1-udef_binary64`
148×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	208	30
2	2913	30

Stop Event

1×	node limit

Counts

4 → 148

Calls

4 calls:

54.0ms	(sqrt.f64 (+.f64 x 1))
54.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
54.0ms	(/.f64 1 (sqrt.f64 x))
54.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify23.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

914×	`fma-neg_binary64`
744×	`cancel-sign-sub-inv_binary64`
439×	`fma-def_binary64`
222×	`distribute-rgt-neg-in_binary64`
202×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	94
1	80	86
2	220	76
3	757	64
4	2431	64

Stop Event

1×	node limit

Counts

156 → 161

prune215.0ms (4.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	150	11	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	11	162

Error

22.8b

Counts

162 → 11

Alt Table

Status	Error	Program
	31.9b	(fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	33.3b	(/.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) (pow.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 3)) (+.f64 (/.f64 1 x) (-.f64 (.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))
	31.4b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (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	(+.f64 (fma.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 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))))
▶	23.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	26.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2))
	31.2b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1) (pow.f64 (+.f64 1 x) -1/2)))
	30.9b	(+.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)))
	25.8b	(*.f64 (+.f64 (sqrt.f64 (pow.f64 x -1/2)) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (-.f64 (sqrt.f64 (pow.f64 x -1/2)) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
	31.9b	(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)))
	31.5b	(fma.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))

Compiler

Compiled 3615 to 2900 computations (19.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 x) -1/2)
✓	0.0b	(/.f64 1 (+.f64 1 x))
✓	0.2b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓	2.8b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series23.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
6.0ms	(pow.f64 (+.f64 1 x) -1/2)
4.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
2.0ms	(/.f64 1 (+.f64 1 x))

rewrite70.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`
146×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	55
1	298	40
2	4536	40

Stop Event

1×	node limit

Counts

4 → 146

Calls

4 calls:

67.0ms	(pow.f64 (+.f64 1 x) -1/2)
67.0ms	(/.f64 1 (+.f64 1 x))
67.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
67.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

simplify41.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

376×	`fma-def_binary64`
311×	`associate-+l+_binary64`
280×	`associate--l+_binary64`
266×	`associate-/r*_binary64`
177×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1464
1	476	1399
2	1442	1232

Stop Event

1×	node limit

Counts

194 → 217

prune234.0ms (5.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	212	5	217
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	223	5	228

Error

5.3b

Counts

228 → 5

Alt Table

Status	Error	Program
	23.1b	(/.f64 (/.f64 (-.f64 (+.f64 -1 (neg.f64 x)) (.f64 x -1)) (.f64 x (+.f64 -1 (neg.f64 x)))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	43.1b	(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))
	23.3b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
▶	5.6b	(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	36.1b	(/.f64 (-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

Compiler

Compiled 5795 to 4364 computations (24.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	0.0b	(pow.f64 (+.f64 1 x) -1/2)
✓	0.1b	(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))
✓	5.6b	(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

series27.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

20.0ms

(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

5.0ms

(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

2.0ms

(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))

rewrite71.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

934×	`prod-diff_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`
135×	`add-sqr-sqrt_binary64`
130×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	332	48
2	4129	48

Stop Event

1×	node limit

Counts

3 → 112

Calls

3 calls:

68.0ms

(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

68.0ms

(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))

68.0ms

(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

simplify38.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary64`
361×	`associate--l+_binary64`
357×	`associate-/r*_binary64`
255×	`times-frac_binary64`
209×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	1554
1	520	1360
2	1685	1181

Stop Event

1×	node limit

Counts

148 → 174

prune239.0ms (5.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	209	7	216
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	214	7	221

Error

Counts

221 → 7

Alt Table

Status	Error	Program
	1.2b	(*.f64 (/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 2)) (/.f64 (/.f64 1 (+.f64 1 x)) (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
▶	0.1b	(*.f64 (/.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (/.f64 (pow.f64 x -1/2) (+.f64 1 x)))
	1.2b	(*.f64 (/.f64 (pow.f64 (/.f64 1 (cbrt.f64 x)) 2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (/.f64 (/.f64 1 (cbrt.f64 x)) (+.f64 1 x)))
	5.9b	(/.f64 (pow.f64 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2) 2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	0.4b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 (+.f64 1 x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
	5.6b	(neg.f64 (/.f64 (/.f64 (/.f64 1 x) (+.f64 1 x)) (neg.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
	6.0b	(pow.f64 (.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (.f64 x (+.f64 1 x))) -1)

Compiler

Compiled 6645 to 5059 computations (23.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series61.0ms (1.4%)

Counts

3 → 8

Calls

3 calls:

29.0ms

(/.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

23.0ms

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

8.0ms

(/.f64 (pow.f64 x -1/2) (+.f64 1 x))

rewrite65.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

782×	`prod-diff_binary64`
127×	`add-sqr-sqrt_binary64`
125×	`log1p-expm1-u_binary64`
125×	`expm1-log1p-u_binary64`
124×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	60
1	260	54
2	3862	54

Stop Event

1×	node limit

Counts

3 → 124

Calls

3 calls:

62.0ms

(/.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

62.0ms

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

62.0ms

(/.f64 (pow.f64 x -1/2) (+.f64 1 x))

simplify27.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

495×	`associate-+l+_binary64`
386×	`associate-+r+_binary64`
376×	`fma-def_binary64`
270×	`associate--l+_binary64`
211×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	683
1	313	503
2	1023	466

Stop Event

1×	node limit

Counts

132 → 139

prune237.0ms (5.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	183	5	188

Error

Counts

188 → 5

Alt Table

Status	Error	Program
	0.4b	(/.f64 (pow.f64 x -1) (*.f64 (+.f64 x 1) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))
	0.5b	(*.f64 (/.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (pow.f64 (/.f64 (pow.f64 x -1/4) (sqrt.f64 (+.f64 x 1))) 2))
	0.1b	(.f64 (/.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 x 1))))
	0.5b	(*.f64 (pow.f64 (/.f64 (pow.f64 x -1/4) (hypot.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4))) 2) (/.f64 (pow.f64 x -1/2) (+.f64 1 x)))
	0.1b	(/.f64 (neg.f64 (pow.f64 x -1/2)) (*.f64 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2)) (+.f64 (neg.f64 x) -1)))

Compiler

Compiled 5262 to 4148 computations (21.2% saved)

regimes1.1s (25.6%)

Accuracy

Total 0.1b remaining (87%)

Threshold costs 0.1b (87%)

Counts

271 → 1

Compiler

Compiled 10852 to 8784 computations (19.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	27	33
2	34	33
3	38	33
4	39	33

Stop Event

1×

saturated

end123.0ms (2.8%)

Compiler: Compiled 161 to 127 computations (21.1% saved)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17

Details

analyze1.0ms (0%)

sample1.7s (37.3%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series31.0ms (0.7%)

rewrite58.0ms (1.3%)

simplify23.0ms (0.5%)

prune215.0ms (4.9%)

localize12.0ms (0.3%)

series23.0ms (0.5%)

rewrite70.0ms (1.6%)

simplify41.0ms (0.9%)

prune234.0ms (5.3%)

localize13.0ms (0.3%)

series27.0ms (0.6%)

rewrite71.0ms (1.6%)

simplify38.0ms (0.9%)

prune239.0ms (5.4%)

localize14.0ms (0.3%)

series61.0ms (1.4%)

rewrite65.0ms (1.5%)

simplify27.0ms (0.6%)

prune237.0ms (5.3%)

regimes1.1s (25.6%)

simplify2.0ms (0.1%)

end123.0ms (2.8%)

Profiling

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17