Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.6s (48.1%)

Results

618.0ms	2014×	body	1024	valid
424.0ms	4403×	body	128	valid
243.0ms	1072×	body	512	valid
88.0ms	546×	body	256	valid
84.0ms	221×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify88.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

27.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite96.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

470×	`fma-def_binary64`
286×	`fma-neg_binary64`
268×	`log-div_binary64`
210×	`egg-rr`
174×	`expm1-udef_binary64`

Counts

3 → 210

Calls

3 calls:

91.0ms	(/.f64 x (+.f64 x 1))
91.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
91.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	195	36
2	2929	36
3	5058	36
0	0	0
1	0	0

simplify65.0ms (2%)

Algorithm

1×	egg-herbie

Rules

773×	`times-frac_binary64`
405×	`fma-neg_binary64`
344×	`cancel-sign-sub-inv_binary64`
292×	`associate-l_binary64`
288×	`fma-def_binary64`

Counts

246 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	475
1	201	443
2	601	430
3	1619	428
4	4294	428
5	5191	428

prune202.0ms (6.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	245	4	249
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	246	4	250

Error

0.0b

Counts

250 → 4

Alt Table

Status	Error	Program
▶	28.3b	(fma.f64 (+.f64 x 1) (neg.f64 (/.f64 1 (-.f64 x 1))) (/.f64 x (+.f64 x 1)))
	33.9b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	34.0b	(neg.f64 (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))
	29.9b	(fma.f64 3 (+.f64 x (pow.f64 x 3)) (fma.f64 x x 1))

Compiler

Compiled 6107 to 4474 computations (26.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	28.3b	(fma.f64 (+.f64 x 1) (neg.f64 (/.f64 1 (-.f64 x 1))) (/.f64 x (+.f64 x 1)))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(fma.f64 (+.f64 x 1) (neg.f64 (/.f64 1 (-.f64 x 1))) (/.f64 x (+.f64 x 1)))

rewrite61.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

928×	`log1p-expm1-u_binary64`
928×	`expm1-log1p-u_binary64`
396×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
93×	`add-log-exp_binary64`

Counts

2 → 60

Calls

2 calls:

60.0ms	(/.f64 1 (-.f64 x 1))
60.0ms	(fma.f64 (+.f64 x 1) (neg.f64 (/.f64 1 (-.f64 x 1))) (/.f64 x (+.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	202	26
2	2369	26
3	6454	26
0	0	0
1	0	0

simplify83.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-def_binary64`
531×	`times-frac_binary64`
479×	`div-sub_binary64`
392×	`sub-neg_binary64`
247×	`distribute-neg-frac_binary64`

Counts

84 → 88

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	369
1	133	340
2	389	336
3	997	333
4	2620	330
5	4094	330
6	4736	330
7	4951	330

prune83.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	134	4	138

Error

0.0b

Counts

138 → 4

Alt Table

Status	Error	Program
✓	28.3b	(fma.f64 (+.f64 x 1) (neg.f64 (/.f64 1 (-.f64 x 1))) (/.f64 x (+.f64 x 1)))
▶	29.9b	(*.f64 (fma.f64 3 x 1) (fma.f64 x x 1))
	33.9b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	34.0b	(neg.f64 (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))

Compiler

Compiled 2642 to 1969 computations (25.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (fma.f64 3 x 1) (fma.f64 x x 1))
✓	0.1b	(fma.f64 3 x 1)

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(*.f64 (fma.f64 3 x 1) (fma.f64 x x 1))
2.0ms	(fma.f64 3 x 1)

rewrite47.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

543×	`log1p-expm1-u_binary64`
543×	`expm1-log1p-u_binary64`
346×	`unpow-prod-down_binary64`
274×	`log-prod_binary64`
178×	`pow2_binary64`

Counts

2 → 58

Calls

2 calls:

45.0ms	(*.f64 (fma.f64 3 x 1) (fma.f64 x x 1))
45.0ms	(fma.f64 3 x 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	134	17
2	1416	17
3	5151	17
0	0	0
1	0	0

simplify121.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

652×	`distribute-rgt-in_binary64`
538×	`unswap-sqr_binary64`
501×	`fma-def_binary64`
453×	`*-commutative_binary64`
416×	`associate-l_binary64`

Counts

82 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	222
1	44	185
2	101	177
3	231	177
4	536	164
5	1542	164
6	2347	164
7	2490	164
8	2761	164
9	3220	164
10	4152	164
11	4698	164
12	4842	164
13	4828	164

prune44.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	70	4	74

Error

0.0b

Counts

74 → 4

Alt Table

Status	Error	Program
✓	28.3b	(fma.f64 (+.f64 x 1) (neg.f64 (/.f64 1 (-.f64 x 1))) (/.f64 x (+.f64 x 1)))
✓	29.9b	(*.f64 (fma.f64 3 x 1) (fma.f64 x x 1))
▶	33.9b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	34.0b	(neg.f64 (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))

Compiler

Compiled 1037 to 772 computations (25.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
✓	0.2b	(/.f64 1 (*.f64 x x))
✓	0.8b	(/.f64 3 (pow.f64 x 3))
✓	9.8b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))

series12.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
3.0ms	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
3.0ms	(/.f64 3 (pow.f64 x 3))
2.0ms	(/.f64 1 (*.f64 x x))

rewrite107.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

633×	`fma-def_binary64`
365×	`fma-neg_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
228×	`egg-rr`

Counts

4 → 228

Calls

4 calls:

101.0ms	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
101.0ms	(/.f64 1 (*.f64 x x))
101.0ms	(/.f64 3 (pow.f64 x 3))
101.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	52
1	282	39
2	3749	39
3	5325	39
0	0	0
1	0	0

simplify74.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

527×	`times-frac_binary64`
465×	`associate-/r*_binary64`
410×	`associate-*l/_binary64`
374×	`fma-def_binary64`
335×	`fma-neg_binary64`

Counts

264 → 241

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	22	456
1	59	438
2	151	438
3	361	438
4	1016	408
5	3828	390
6	4523	390
7	5055	390

prune186.0ms (5.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	241	4	245

Error

Counts

245 → 4

Alt Table

Status	Error	Program
✓	28.3b	(fma.f64 (+.f64 x 1) (neg.f64 (/.f64 1 (-.f64 x 1))) (/.f64 x (+.f64 x 1)))
✓	29.9b	(*.f64 (fma.f64 3 x 1) (fma.f64 x x 1))
	34.0b	(fma.f64 -3 (/.f64 1 x) (neg.f64 (fma.f64 3 (pow.f64 x -3) (pow.f64 x -2))))
	33.9b	(+.f64 (-.f64 (/.f64 -3 x) (pow.f64 x -2)) (*.f64 -3 (pow.f64 x -3)))

Compiler

Compiled 5858 to 4479 computations (23.5% saved)

regimes268.0ms (8.2%)

Accuracy

Total 0.2b remaining (83.8%)

Threshold costs 0.2b (83.8%)

Counts

92 → 2

Compiler

Compiled 3238 to 2464 computations (23.9% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	87
1	40	87
2	51	87
3	61	87
4	68	87
5	71	87
6	72	87
7	70	87

end90.0ms (2.8%)

Compiler: Compiled 175 to 132 computations (24.6% saved)

Details

analyze5.0ms (0.2%)

sample1.6s (48.1%)

simplify88.0ms (2.7%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series8.0ms (0.2%)

rewrite96.0ms (3%)

simplify65.0ms (2%)

prune202.0ms (6.2%)

localize8.0ms (0.2%)

series7.0ms (0.2%)

rewrite61.0ms (1.9%)

simplify83.0ms (2.5%)

prune83.0ms (2.6%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite47.0ms (1.4%)

simplify121.0ms (3.7%)

prune44.0ms (1.4%)

localize9.0ms (0.3%)

series12.0ms (0.4%)

rewrite107.0ms (3.3%)

simplify74.0ms (2.3%)

prune186.0ms (5.7%)

regimes268.0ms (8.2%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.2%)

end90.0ms (2.8%)

Profiling