Details

analyze103.0ms (2.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.4s (29.6%)

Results

648.0ms	6454×	body	128	valid
237.0ms	721×	body	512	valid
237.0ms	630×	body	1024	valid
134.0ms	444×	body	256	valid
2.0ms	7×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify197.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1996×	`fma-def_binary64`
1626×	`fma-neg_binary64`
1098×	`div-sub_binary64`
733×	`sub-neg_binary64`
664×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	102	14
4	274	14
5	652	14
6	1272	14
7	1697	14
8	2416	14
9	2933	14
10	3278	14
11	3461	14
12	1980	14
13	1996	14
14	2659	14
15	2539	14
16	2497	14
17	2531	14
18	2531	14
19	4723	14
20	4903	14
21	5942	14

prune4.0ms (0.1%)

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

Error

16.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	24.1b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
▶	16.8b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	16.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series20.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
8.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite88.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`log-prod_binary64`
270×	`prod-diff_binary64`
215×	`fma-def_binary64`
172×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`

Counts

2 → 67

Calls

2 calls:

87.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
86.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	193	24
2	2481	24
3	4892	24
4	5106	24

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-neg_binary64`
486×	`associate--l+_binary64`
453×	`times-frac_binary64`
420×	`associate--r+_binary64`
353×	`associate-+l+_binary64`

Counts

115 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1015
1	233	980
2	818	936
3	3450	893
4	4788	893
5	5485	893

prune174.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	103	5	108

Error

0.1b

Counts

108 → 5

Alt Table

Status	Error	Program
▶	16.9b	(+.f64 1 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)))
	30.2b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
	39.1b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 y 1)) 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 y 1)) 1)))))
	33.9b	(fma.f64 y (-.f64 x (-.f64 (fma.f64 y x 1) y)) 1)
✓	16.8b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 1943 to 1366 computations (29.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
✓	0.0b	(/.f64 y (+.f64 1 y))
✓	3.0b	(+.f64 1 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)))

series25.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

13.0ms	(+.f64 1 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)))
10.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
2.0ms	(/.f64 y (+.f64 1 y))

rewrite80.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

488×	`fma-def_binary64`
237×	`fma-neg_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
197×	`log-div_binary64`

Counts

3 → 187

Calls

3 calls:

76.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
76.0ms	(/.f64 y (+.f64 1 y))
76.0ms	(+.f64 1 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	228	34
2	3135	34
3	5140	34

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-neg_binary64`
519×	`associate--l+_binary64`
413×	`associate--r+_binary64`
335×	`associate-+l+_binary64`
327×	`fma-def_binary64`

Counts

247 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1139
1	263	1116
2	906	994
3	3547	978
4	4800	978
5	4968	978

prune218.0ms (4.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	235	2	237
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	237	5	242

Error

0.1b

Counts

242 → 5

Alt Table

Status	Error	Program
▶	16.9b	(+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) (+.f64 x -1))))
	30.2b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
	17.3b	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (+.f64 1 y)) 2)) (/.f64 (+.f64 x -1) (cbrt.f64 (+.f64 1 y))) 1)
	39.1b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 y 1)) 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 y 1)) 1)))))
✓	16.8b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 4568 to 3193 computations (30.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 y) (+.f64 x -1))
✓	0.1b	(/.f64 y (/.f64 (+.f64 1 y) (+.f64 x -1)))
✓	3.0b	(+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) (+.f64 x -1))))

series47.0ms (1%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(/.f64 (+.f64 1 y) (+.f64 x -1))
11.0ms	(+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) (+.f64 x -1))))
10.0ms	(/.f64 y (/.f64 (+.f64 1 y) (+.f64 x -1)))

rewrite73.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

741×	`prod-diff_binary64`
204×	`log1p-udef_binary64`
117×	`egg-rr`
114×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`

Counts

3 → 117

Calls

3 calls:

71.0ms	(/.f64 (+.f64 1 y) (+.f64 x -1))
71.0ms	(/.f64 y (/.f64 (+.f64 1 y) (+.f64 x -1)))
71.0ms	(+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) (+.f64 x -1))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	228	37
2	3207	37
3	5157	37

simplify181.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-def_binary64`
496×	`+-commutative_binary64`
492×	`associate--r+_binary64`
459×	`associate--l+_binary64`
370×	`times-frac_binary64`

Counts

189 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	1540
1	391	1515
2	1358	1385
3	4503	1385
4	4883	1385
5	5261	1385

prune123.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	174	5	179

Error

0.1b

Counts

179 → 5

Alt Table

Status	Error	Program
✓	16.9b	(+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) (+.f64 x -1))))
	30.2b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
▶	17.3b	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (+.f64 1 y)) 2)) (/.f64 (+.f64 x -1) (cbrt.f64 (+.f64 1 y))) 1)
	39.1b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 y 1)) 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 y 1)) 1)))))
✓	16.8b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 3292 to 2324 computations (29.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (+.f64 x -1) (cbrt.f64 (+.f64 1 y)))
✓	0.3b	(cbrt.f64 (+.f64 1 y))
✓	0.3b	(pow.f64 (cbrt.f64 (+.f64 1 y)) 2)
✓	17.0b	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (+.f64 1 y)) 2)) (/.f64 (+.f64 x -1) (cbrt.f64 (+.f64 1 y))) 1)

series246.0ms (5.2%)

Counts

4 → 72

Calls

4 calls:

168.0ms	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (+.f64 1 y)) 2)) (/.f64 (+.f64 x -1) (cbrt.f64 (+.f64 1 y))) 1)
67.0ms	(/.f64 (+.f64 x -1) (cbrt.f64 (+.f64 1 y)))
6.0ms	(pow.f64 (cbrt.f64 (+.f64 1 y)) 2)
4.0ms	(cbrt.f64 (+.f64 1 y))

rewrite109.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
224×	`fma-def_binary64`
204×	`prod-diff_binary64`
198×	`fma-udef_binary64`

Counts

4 → 102

Calls

4 calls:

107.0ms	(/.f64 (+.f64 x -1) (cbrt.f64 (+.f64 1 y)))
107.0ms	(cbrt.f64 (+.f64 1 y))
107.0ms	(pow.f64 (cbrt.f64 (+.f64 1 y)) 2)
107.0ms	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (+.f64 1 y)) 2)) (/.f64 (+.f64 x -1) (cbrt.f64 (+.f64 1 y))) 1)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	279	43
2	3408	43
3	4941	43
4	4917	43

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Rules

672×	`cancel-sign-sub-inv_binary64`
558×	`fma-neg_binary64`
490×	`times-frac_binary64`
350×	`sub-neg_binary64`
271×	`fma-def_binary64`

Counts

174 → 203

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	2644
1	812	2449
2	2707	2116
3	4342	1833
4	5167	1833

prune257.0ms (5.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	251	5	256

Error

0.1b

Counts

256 → 5

Alt Table

Status	Error	Program
✓	16.9b	(+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) (+.f64 x -1))))
	30.2b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
✓	17.3b	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (+.f64 1 y)) 2)) (/.f64 (+.f64 x -1) (cbrt.f64 (+.f64 1 y))) 1)
	39.1b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 y 1)) 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 y 1)) 1)))))
✓	16.8b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 7061 to 5544 computations (21.5% saved)

regimes921.0ms (19.6%)

Accuracy

Total 0.0b remaining (28.6%)

Threshold costs 0.0b (28.6%)

Counts

106 → 3

Compiler

Compiled 8921 to 6628 computations (25.7% saved)

bsearch39.0ms (0.8%)

Steps

Iters	Range		Point
9	83.88382976737913	5515880.36144037	11649.159016303365
8	-10106929.118142124	-15760.002573564716	-16205.4911207915

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`*-commutative_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	127
1	47	127
2	60	127
3	78	127
4	97	127
5	110	127
6	116	127
7	117	127
8	114	127

end122.0ms (2.6%)

Compiler: Compiled 283 to 185 computations (34.6% saved)

Details

analyze103.0ms (2.2%)

sample1.4s (29.6%)

simplify197.0ms (4.2%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series20.0ms (0.4%)

rewrite88.0ms (1.9%)

simplify76.0ms (1.6%)

prune174.0ms (3.7%)

localize6.0ms (0.1%)

series25.0ms (0.5%)

rewrite80.0ms (1.7%)

simplify77.0ms (1.6%)

prune218.0ms (4.6%)

localize7.0ms (0.2%)

series47.0ms (1%)

rewrite73.0ms (1.6%)

simplify181.0ms (3.9%)

prune123.0ms (2.6%)

localize11.0ms (0.2%)

series246.0ms (5.2%)

rewrite109.0ms (2.3%)

simplify94.0ms (2%)

prune257.0ms (5.5%)

regimes921.0ms (19.6%)

bsearch39.0ms (0.8%)

simplify7.0ms (0.1%)

end122.0ms (2.6%)

Profiling