Details

analyze132.0ms (4.5%)

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
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
50%	50%	0.1%	7
67.1%	32.8%	0.1%	8
74.9%	25%	0.1%	9
83.9%	16%	0.1%	10
87.4%	12.5%	0.1%	11
92%	7.9%	0.1%	12
93.7%	6.2%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample880.0ms (29.8%)

Results

837.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify30.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1119×	`fma-neg_binary64`
675×	`div-sub_binary64`
519×	`fma-def_binary64`
403×	`associate-/l*_binary64`
249×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	28	14
3	41	14
4	60	14
5	96	14
6	172	14
7	254	14
8	492	14
9	1053	14
10	1774	14
11	3750	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
▶	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))

Compiler

Compiled 73 to 52 computations (28.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 (*.f64 x y) 2))
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
✓	6.4b	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

series23.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

10.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
8.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))
4.0ms	(+.f64 1 (/.f64 (*.f64 x y) 2))

rewrite80.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

789×	`prod-diff_binary64`
202×	`log1p-udef_binary64`
182×	`egg-rr`
113×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	230	33
2	3221	33

Stop Event

1×	node limit

Counts

3 → 182

Calls

3 calls:

75.0ms	(+.f64 1 (/.f64 (*.f64 x y) 2))
75.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
75.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

simplify55.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
400×	`distribute-rgt-neg-in_binary64`
244×	`fma-def_binary64`
222×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1204
1	210	1190
2	689	1180
3	2916	1167

Stop Event

1×	node limit

Counts

254 → 219

prune205.0ms (7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	217	4	221

Error

Counts

221 → 4

Alt Table

Status	Error	Program
	17.5b	(-.f64 x (.f64 (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (*.f64 x 1/2)))))
▶	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
	9.2b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))))

Compiler

Compiled 7285 to 4306 computations (40.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
✓	0.0b	(fma.f64 x -1/2 (/.f64 -1 y))
✓	0.1b	(/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y)))

series21.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

8.0ms	(/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y)))
8.0ms	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
5.0ms	(fma.f64 x -1/2 (/.f64 -1 y))

rewrite60.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`prod-diff_binary64`
204×	`fma-def_binary64`
178×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`
152×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	198	33
2	2589	33

Stop Event

1×	node limit

Counts

3 → 149

Calls

3 calls:

57.0ms	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
57.0ms	(fma.f64 x -1/2 (/.f64 -1 y))
57.0ms	(/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y)))

simplify45.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

644×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
236×	`fma-def_binary64`
216×	`associate-r_binary64`
210×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	1270
1	214	1220
2	704	1174
3	2960	1165

Stop Event

1×	node limit

Counts

221 → 186

prune152.0ms (5.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	186	4	190

Error

Counts

190 → 4

Alt Table

Status	Error	Program
	17.5b	(-.f64 x (.f64 (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (*.f64 x 1/2)))))
✓	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
▶	9.2b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))))

Compiler

Compiled 4221 to 3122 computations (26% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))))
✓	0.0b	(log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))
✓	0.5b	(expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1))))
✓	6.4b	(/.f64 y (fma.f64 (*.f64 y x) 1/2 1))

series51.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

22.0ms	(log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))
11.0ms	(/.f64 y (fma.f64 (*.f64 y x) 1/2 1))
9.0ms	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))))
8.0ms	(expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1))))

rewrite81.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

717×	`prod-diff_binary64`
245×	`fma-def_binary64`
241×	`egg-rr`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	212	49
2	2745	49

Stop Event

1×	node limit

Counts

4 → 241

Calls

4 calls:

76.0ms	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))))
76.0ms	(log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))
76.0ms	(expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1))))
76.0ms	(/.f64 y (fma.f64 (*.f64 y x) 1/2 1))

simplify63.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

674×	`times-frac_binary64`
392×	`cancel-sign-sub-inv_binary64`
229×	`sub-neg_binary64`
206×	`unswap-sqr_binary64`
204×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2903
1	646	2869
2	2586	2866

Stop Event

1×	node limit

Counts

337 → 266

prune298.0ms (10.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	266	0	266
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	266	4	270

Error

Counts

270 → 4

Alt Table

Status	Error	Program
▶	17.5b	(-.f64 x (.f64 (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (*.f64 x 1/2)))))
✓	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
✓	9.2b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))))

Compiler

Compiled 9048 to 6143 computations (32.1% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 y x) 2)
✓	2.0b	(/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3)))
✓	2.8b	(-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2)))
✓	22.0b	(.f64 (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (*.f64 x 1/2))))

series127.0ms (4.3%)

Counts

4 → 96

Calls

4 calls:

59.0ms	(/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3)))
30.0ms	(pow.f64 (*.f64 y x) 2)
27.0ms	(.f64 (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (*.f64 x 1/2))))
11.0ms	(-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2)))

rewrite50.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
193×	`add-sqr-sqrt_binary64`
189×	`add-cbrt-cube_binary64`
182×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	85
1	426	81

Stop Event

1×	node limit

Counts

4 → 130

Calls

4 calls:

47.0ms	(pow.f64 (*.f64 y x) 2)
47.0ms	(/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3)))
47.0ms	(-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (.f64 x 1/2)))
47.0ms	(.f64 (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (*.f64 x 1/2))))

simplify59.0ms (2%)

Algorithm

1×	egg-herbie

Rules

653×	`times-frac_binary64`
475×	`associate-l_binary64`
470×	`associate-r_binary64`
319×	`associate-/r*_binary64`
277×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1984
1	302	1960
2	970	1910
3	4467	1910

Stop Event

1×	node limit

Counts

226 → 169

prune217.0ms (7.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	169	4	173

Error

Counts

173 → 4

Alt Table

Status	Error	Program
✓	17.5b	(-.f64 x (.f64 (/.f64 y (+.f64 1 (pow.f64 (.f64 y (.f64 x 1/2)) 3))) (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 y x) 2) 1/4)) (.f64 y (*.f64 x 1/2)))))
✓	0.1b	(-.f64 x (/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y))))
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
✓	9.2b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 (*.f64 y x) 1/2 1)))))

Compiler

Compiled 6297 to 4232 computations (32.8% saved)

regimes205.0ms (7%)

Accuracy

Total 0.0b remaining (93.3%)

Threshold costs 0.0b (93.3%)

Counts

65 → 1

Compiler

Compiled 3536 to 2537 computations (28.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	14
2	20	14
3	24	14
4	27	14
5	28	14

Stop Event

1×

saturated

end72.0ms (2.4%)

Compiler: Compiled 94 to 67 computations (28.7% saved)

Details

analyze132.0ms (4.5%)

sample880.0ms (29.8%)

simplify30.0ms (1%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series23.0ms (0.8%)

rewrite80.0ms (2.7%)

simplify55.0ms (1.9%)

prune205.0ms (7%)

localize7.0ms (0.3%)

series21.0ms (0.7%)

rewrite60.0ms (2%)

simplify45.0ms (1.5%)

prune152.0ms (5.2%)

localize8.0ms (0.3%)

series51.0ms (1.7%)

rewrite81.0ms (2.8%)

simplify63.0ms (2.1%)

prune298.0ms (10.1%)

localize16.0ms (0.5%)

series127.0ms (4.3%)

rewrite50.0ms (1.7%)

simplify59.0ms (2%)

prune217.0ms (7.4%)

regimes205.0ms (7%)

simplify2.0ms (0.1%)

end72.0ms (2.4%)

Profiling