Details

analyze498.0ms (8.7%)

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)

sample2.1s (37.1%)

Results

1.7s	8255×	body	128	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify228.0ms (4%)

Algorithm

1×	egg-herbie

Rules

2174×	`fma-neg_binary64`
1504×	`div-sub_binary64`
895×	`associate-/l/_binary64`
827×	`fma-def_binary64`
818×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	28	14
3	41	14
4	57	14
5	91	14
6	134	14
7	193	14
8	356	14
9	521	14
10	825	14
11	1475	14
12	2002	14
13	1877	14
14	1931	14
15	1961	14
16	1967	14
17	1967	14
18	2590	14
19	2366	14
20	2366	14
21	3254	14
22	4052	14
23	4024	14
24	4504	14
25	4470	14
26	4706	14
27	4913	14

prune9.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 47 to 31 computations (34% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
✓	7.8b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

series35.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))
16.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

rewrite175.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

692×	`prod-diff_binary64`
218×	`fma-def_binary64`
182×	`egg-rr`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Counts

2 → 182

Calls

2 calls:

160.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
160.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	198	25
2	2507	25
3	4853	25
4	5158	25
0	0	0
1	0	0

simplify126.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

930×	`times-frac_binary64`
635×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`
402×	`distribute-rgt-neg-in_binary64`
392×	`distribute-lft-neg-in_binary64`

Counts

230 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	1030
1	199	1016
2	643	1006
3	2343	993
4	4887	993
5	6134	993

prune505.0ms (8.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	211	4	215

Error

Counts

215 → 4

Alt Table

Status	Error	Program
	22.4b	(-.f64 x (/.f64 2 x))
	27.6b	(-.f64 x (fma.f64 (.f64 (.f64 y y) x) -1/2 y))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
▶	0.4b	(-.f64 x (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))))

Compiler

Compiled 7130 to 4693 computations (34.2% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 y)
✓	0.6b	(/.f64 1 (fma.f64 x (/.f64 y 2) 1))
✓	2.4b	(*.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))
✓	4.8b	(.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))

series205.0ms (3.6%)

Counts

4 → 84

Calls

4 calls:

76.0ms	(*.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))
75.0ms	(cbrt.f64 y)
27.0ms	(.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))
26.0ms	(/.f64 1 (fma.f64 x (/.f64 y 2) 1))

rewrite117.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

553×	`log-prod_binary64`
203×	`pow1/3_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
181×	`pow3_binary64`

Counts

4 → 110

Calls

4 calls:

114.0ms	(cbrt.f64 y)
114.0ms	(/.f64 1 (fma.f64 x (/.f64 y 2) 1))
114.0ms	(*.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))
114.0ms	(.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	41
1	250	38
2	2730	38
3	4944	38
0	0	0
1	0	0

simplify150.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-neg_binary64`
627×	`associate-l_binary64`
474×	`fma-def_binary64`
369×	`associate-/r*_binary64`
368×	`cancel-sign-sub-inv_binary64`

Counts

194 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	2272
1	478	2150
2	1519	2118
3	4865	2098
4	5340	2098

prune313.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	191	4	195

Error

Counts

195 → 4

Alt Table

Status	Error	Program
▶	22.4b	(-.f64 x (/.f64 2 x))
	27.6b	(-.f64 x (fma.f64 (.f64 (.f64 y y) x) -1/2 y))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
✓	0.4b	(-.f64 x (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))))

Compiler

Compiled 4530 to 3020 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 2 x))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(-.f64 x (/.f64 2 x))

rewrite83.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

628×	`log1p-expm1-u_binary64`
628×	`expm1-log1p-u_binary64`
478×	`prod-diff_binary64`
110×	`log1p-udef_binary64`
61×	`add-sqr-sqrt_binary64`

Counts

1 → 60

Calls

1 calls:

79.0ms

(-.f64 x (/.f64 2 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	119	7
2	1574	7
3	4928	7
0	0	0
1	0	0

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

66×	`fma-neg_binary64`
65×	`fma-def_binary64`
30×	`associate-/r*_binary64`
25×	`cancel-sign-sub-inv_binary64`
23×	`associate-/l*_binary64`

Counts

72 → 63

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	69
1	19	69
2	28	69
3	45	69
4	58	69
5	83	69
6	114	69
7	143	69
8	185	69
9	223	69
10	279	69
11	301	69
12	319	69
13	251	69

prune78.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	63	4	67

Error

Counts

67 → 4

Alt Table

Status	Error	Program
✓	22.4b	(-.f64 x (/.f64 2 x))
▶	27.6b	(-.f64 x (fma.f64 (.f64 (.f64 y y) x) -1/2 y))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
✓	0.4b	(-.f64 x (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))))

Compiler

Compiled 1013 to 693 computations (31.6% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (fma.f64 (.f64 (.f64 y y) x) -1/2 y))
✓	0.0b	(fma.f64 (.f64 (.f64 y y) x) -1/2 y)
✓	6.6b	(.f64 (.f64 y y) x)

series59.0ms (1%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(fma.f64 (.f64 (.f64 y y) x) -1/2 y)
19.0ms	(-.f64 x (fma.f64 (.f64 (.f64 y y) x) -1/2 y))
14.0ms	(.f64 (.f64 y y) x)

rewrite117.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

852×	`log1p-expm1-u_binary64`
852×	`expm1-log1p-u_binary64`
487×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
87×	`egg-rr`

Counts

3 → 87

Calls

3 calls:

111.0ms	(-.f64 x (fma.f64 (.f64 (.f64 y y) x) -1/2 y))
111.0ms	(fma.f64 (.f64 (.f64 y y) x) -1/2 y)
111.0ms	(.f64 (.f64 y y) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	32
1	174	32
2	2132	32
3	6105	32
0	0	0
1	0	0

simplify324.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1770×	`fma-def_binary64`
837×	`cube-prod_binary64`
712×	`distribute-rgt-in_binary64`
660×	`fabs-mul_binary64`
629×	`distribute-rgt-neg-in_binary64`

Counts

159 → 104

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	21	732
1	49	728
2	104	688
3	255	688
4	703	658
5	1710	658
6	2196	658
7	2626	658
8	3318	658
9	3344	658
10	2871	658
11	4968	658
12	4787	658
13	3392	658
14	3284	658
15	4013	658
16	4579	658
17	4883	658
18	4703	658

prune175.0ms (3.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	104	4	108

Error

Counts

108 → 4

Alt Table

Status	Error	Program
✓	22.4b	(-.f64 x (/.f64 2 x))
✓	27.6b	(-.f64 x (fma.f64 (.f64 (.f64 y y) x) -1/2 y))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
✓	0.4b	(-.f64 x (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))))

Compiler

Compiled 2023 to 876 computations (56.7% saved)

regimes139.0ms (2.4%)

Accuracy

Total 0.0b remaining (80.5%)

Threshold costs 0.0b (80.5%)

Counts

22 → 1

Compiler

Compiled 689 to 476 computations (30.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	19	14
3	23	14
4	26	14
5	27	14
6	26	14

end141.0ms (2.5%)

Compiler: Compiled 75 to 50 computations (33.3% saved)

Iter	Nodes	Cost
0	9	69
1	19	69
2	28	69
3	45	69
4	58	69
5	83	69
6	114	69
7	143	69
8	185	69
9	223	69
10	279	69
11	301	69
12	319	69
13	251	69

Iter	Nodes	Cost
0	9	69
1	19	69
2	28	69
3	45	69
4	58	69
5	83	69
6	114	69
7	143	69
8	185	69
9	223	69
10	279	69
11	301	69
12	319	69
13	251	69

Details

analyze498.0ms (8.7%)

sample2.1s (37.1%)

simplify228.0ms (4%)

prune9.0ms (0.2%)

localize16.0ms (0.3%)

series35.0ms (0.6%)

rewrite175.0ms (3.1%)

simplify126.0ms (2.2%)

prune505.0ms (8.8%)

localize26.0ms (0.5%)

series205.0ms (3.6%)

rewrite117.0ms (2.1%)

simplify150.0ms (2.6%)

prune313.0ms (5.5%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite83.0ms (1.5%)

simplify42.0ms (0.7%)

prune78.0ms (1.4%)

localize14.0ms (0.2%)

series59.0ms (1%)

rewrite117.0ms (2%)

simplify324.0ms (5.7%)

prune175.0ms (3.1%)

regimes139.0ms (2.4%)

simplify4.0ms (0.1%)

end141.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	9	69
1	19	69
2	28	69
3	45	69
4	58	69
5	83	69
6	114	69
7	143	69
8	185	69
9	223	69
10	279	69
11	301	69
12	319	69
13	251	69