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)

sample1.8s (43.8%)

Results

860.0ms	2250×	body	1024	valid
482.0ms	4417×	body	128	valid
281.0ms	1054×	body	512	valid
95.0ms	535×	body	256	valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify88.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

534×	`rules-10-rev_binary64`
423×	`rules-20_binary64`
415×	`cube-div_binary64`
350×	`fma-def_binary64`
331×	`rules-5-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	20	17
2	26	17
3	51	17
4	138	17
5	444	17
6	1448	17
7	4069	17
8	4364	17
9	4814	17
10	5150	17

prune2.0ms (0.1%)

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

21.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.5b	(-.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)))
✓	0.2b	(/.f64 1 (sqrt.f64 x))
✓	5.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series46.0ms (1.1%)

Counts

4 → 8

Calls

4 calls:

15.0ms	(/.f64 1 (sqrt.f64 x))
14.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(sqrt.f64 (+.f64 x 1))

rewrite104.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 171

Calls

4 calls:

102.0ms	(sqrt.f64 (+.f64 x 1))
102.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
102.0ms	(/.f64 1 (sqrt.f64 x))
102.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	217	30
2	2726	30
3	4939	30
4	4913	30
0	0	0
1	0	0

simplify65.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-neg_binary64`
444×	`rules-11_binary64`
398×	`fma-def_binary64`
391×	`rules-21_binary64`
279×	`rules-20_binary64`

Counts

179 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	94
1	80	84
2	291	81
3	1086	76
4	4728	76
5	4986	76
6	4932	76

prune234.0ms (5.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	169	14	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	14	184

Error

20.6b

Counts

184 → 14

Alt Table

Status	Error	Program
	31.6b	(fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	24.6b	(/.f64 (/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
	31.7b	(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)))
	30.5b	(+.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))))
	31.1b	(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)))
	31.0b	(+.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)))
	31.0b	(/.f64 (/.f64 (fma.f64 (pow.f64 x -1/2) (sqrt.f64 (+.f64 1 x)) -1) (pow.f64 (+.f64 1 x) 1/4)) (pow.f64 (+.f64 1 x) 1/4))
	30.8b	(+.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)))
	31.1b	(/.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))))
	31.0b	(/.f64 (fma.f64 (pow.f64 x -1/2) (sqrt.f64 (+.f64 1 x)) -1) (sqrt.f64 (+.f64 1 x)))
▶	24.3b	(/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (sqrt.f64 x))
	32.0b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 x) -3) (pow.f64 (sqrt.f64 (+.f64 1 x)) -3)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 (pow.f64 x -1/2) (sqrt.f64 (+.f64 1 x))))))
	31.1b	(+.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))))
	30.9b	(+.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))))

Compiler

Compiled 3973 to 3174 computations (20.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 x) -1/2)
✓	0.2b	(/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (sqrt.f64 x))
✓	0.2b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))
✓	13.8b	(-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2)))

series48.0ms (1.1%)

Counts

4 → 22

Calls

4 calls:

18.0ms	(/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (sqrt.f64 x))
14.0ms	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))
12.0ms	(-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2)))
4.0ms	(pow.f64 (+.f64 1 x) -1/2)

rewrite92.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

807×	`fma-neg_binary64`
592×	`prod-diff_binary64`
237×	`egg-rr`
173×	`expm1-udef_binary64`
173×	`log1p-udef_binary64`

Counts

4 → 237

Calls

4 calls:

87.0ms	(pow.f64 (+.f64 1 x) -1/2)
87.0ms	(/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (sqrt.f64 x))
87.0ms	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))
87.0ms	(-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	54
1	238	47
2	2810	47
3	5121	47
0	0	0
1	0	0

simplify53.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-def_binary64`
292×	`fma-neg_binary64`
242×	`rules-4_binary64`
219×	`rules-11_binary64`
204×	`rules-15-rev_binary64`

Counts

259 → 270

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	489
1	225	477
2	934	396
3	4476	379
4	5303	379

prune233.0ms (5.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	269	1	270
Fresh	12	1	13
Picked	0	1	1
Done	0	0	0
Total	281	3	284

Error

0.1b

Counts

284 → 3

Alt Table

Status	Error	Program
✓	24.3b	(/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (sqrt.f64 x))
▶	30.8b	(/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x))) (sqrt.f64 x))
	31.0b	(+.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)))

Compiler

Compiled 6729 to 4751 computations (29.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))
✓	0.2b	(/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x))) (sqrt.f64 x))
✓	0.4b	(/.f64 3/8 (*.f64 x x))

series21.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

15.0ms	(/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x))) (sqrt.f64 x))
3.0ms	(-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))
2.0ms	(/.f64 3/8 (*.f64 x x))

rewrite71.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`fma-neg_binary64`
432×	`prod-diff_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
116×	`egg-rr`

Counts

3 → 116

Calls

3 calls:

68.0ms	(-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))
68.0ms	(/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x))) (sqrt.f64 x))
68.0ms	(/.f64 3/8 (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	243	38
2	2989	38
3	4878	38
0	0	0
1	0	0

simplify87.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-neg_binary64`
518×	`rules-20_binary64`
483×	`fma-def_binary64`
335×	`rules-15-rev_binary64`
154×	`fma-udef_binary64`

Counts

140 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	216
1	32	216
2	71	216
3	234	189
4	863	189
5	1867	189
6	4693	189
7	4898	189
8	4994	189
9	4952	189

prune97.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	116	10	126

Error

0.0b

Counts

126 → 10

Alt Table

Status	Error	Program
	31.2b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))) 3) (sqrt.f64 x))
	30.8b	(.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (.f64 x x))) (/.f64 1 (sqrt.f64 x)))
	31.0b	(+.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)))
	31.2b	(/.f64 (/.f64 (/.f64 (-.f64 1/2 (.f64 x (/.f64 3/8 (.f64 x x)))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (sqrt.f64 x))
✓	24.3b	(/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (sqrt.f64 x))
	50.3b	(/.f64 (/.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 27/512 (pow.f64 (.f64 x x) 3))) (+.f64 (pow.f64 (/.f64 1/2 x) 2) (+.f64 (pow.f64 (/.f64 3/8 (.f64 x x)) 2) (.f64 (/.f64 3/8 (.f64 x x)) (/.f64 1/2 x))))) (sqrt.f64 x))
	31.1b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x))) (sqrt.f64 x))) 2)
	31.1b	(.f64 (sqrt.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (.f64 x x)))) (/.f64 (sqrt.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))) (sqrt.f64 x)))
	31.2b	(.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (.f64 x x))) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x))) (sqrt.f64 x))) 2))
▶	30.2b	(/.f64 (fabs.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))) (sqrt.f64 x))

Compiler

Compiled 2723 to 1687 computations (38% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))
✓	0.2b	(/.f64 (fabs.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))) (sqrt.f64 x))
	0.4b	(/.f64 3/8 (*.f64 x x))

series27.0ms (0.7%)

Counts

1 → 0

Calls

1 calls:

27.0ms

(/.f64 (fabs.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))) (sqrt.f64 x))

rewrite63.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

750×	`fma-neg_binary64`
433×	`prod-diff_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
114×	`add-sqr-sqrt_binary64`

Counts

1 → 34

Calls

1 calls:

62.0ms

(/.f64 (fabs.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	266	18
2	3019	18
3	4889	18
0	0	0
1	0	0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune101.0ms (2.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	123	10	133

Error

0.0b

Counts

133 → 10

Alt Table

Status	Error	Program
	31.2b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))) 3) (sqrt.f64 x))
	30.8b	(.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (.f64 x x))) (/.f64 1 (sqrt.f64 x)))
	31.0b	(+.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)))
	31.2b	(/.f64 (/.f64 (/.f64 (-.f64 1/2 (.f64 x (/.f64 3/8 (.f64 x x)))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (sqrt.f64 x))
✓	24.3b	(/.f64 (-.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 x) -1/2))) (sqrt.f64 x))
	50.3b	(/.f64 (/.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 27/512 (pow.f64 (.f64 x x) 3))) (+.f64 (pow.f64 (/.f64 1/2 x) 2) (+.f64 (pow.f64 (/.f64 3/8 (.f64 x x)) 2) (.f64 (/.f64 3/8 (.f64 x x)) (/.f64 1/2 x))))) (sqrt.f64 x))
	31.1b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x))) (sqrt.f64 x))) 2)
	31.1b	(.f64 (sqrt.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (.f64 x x)))) (/.f64 (sqrt.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))) (sqrt.f64 x)))
	31.2b	(.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (.f64 x x))) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x))) (sqrt.f64 x))) 2))
✓	30.2b	(/.f64 (fabs.f64 (-.f64 (/.f64 1/2 x) (/.f64 3/8 (*.f64 x x)))) (sqrt.f64 x))

Compiler

Compiled 2604 to 1626 computations (37.6% saved)

regimes682.0ms (16.3%)

Accuracy

Total 0.2b remaining (63.5%)

Threshold costs 0.2b (63.5%)

Counts

229 → 2

Compiler

Compiled 8082 to 6532 computations (19.2% saved)

bsearch7.0ms (0.2%)

Compiler: Compiled 12 to 10 computations (16.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	89
1	35	89
2	34	89

end185.0ms (4.4%)

Compiler: Compiled 342 to 254 computations (25.7% saved)

Details

analyze1.0ms (0%)

sample1.8s (43.8%)

simplify88.0ms (2.1%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series46.0ms (1.1%)

rewrite104.0ms (2.5%)

simplify65.0ms (1.6%)

prune234.0ms (5.6%)

localize9.0ms (0.2%)

series48.0ms (1.1%)

rewrite92.0ms (2.2%)

simplify53.0ms (1.3%)

prune233.0ms (5.6%)

localize7.0ms (0.2%)

series21.0ms (0.5%)

rewrite71.0ms (1.7%)

simplify87.0ms (2.1%)

prune97.0ms (2.3%)

localize8.0ms (0.2%)

series27.0ms (0.7%)

rewrite63.0ms (1.5%)

simplify7.0ms (0.2%)

prune101.0ms (2.4%)

regimes682.0ms (16.3%)

bsearch7.0ms (0.2%)

simplify2.0ms (0.1%)

end185.0ms (4.4%)

Profiling