Details

analyze422.0ms (7.5%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
34.3%	62.4%	3.3%	9
42.1%	49.9%	7.9%	10
53.8%	37.8%	8.3%	11
56.2%	33%	10.9%	12
60.3%	25.6%	14.1%	13
66.4%	19.4%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.1s (19.7%)

Results

844.0ms	8256×	body	128	valid
75.0ms	730×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
164×	`distribute-lft-in_binary64`
139×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	47	11
3	132	11
4	334	11
5	640	11
6	965	11
7	1254	11
8	1262	11
9	1262	11
10	1191	11

prune3.0ms (0%)

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

5.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.6b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.2b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series13.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

rewrite52.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
83×	`add-sqr-sqrt_binary64`
76×	`add-cbrt-cube_binary64`

Counts

1 → 21

Calls

1 calls:

51.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	163	11
2	2007	11
3	5600	11
0	0	0
1	0	0

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-neg_binary64`
383×	`fma-def_binary64`
129×	`cancel-sign-sub-inv_binary64`
112×	`distribute-rgt-in_binary64`
97×	`unsub-neg_binary64`

Counts

57 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	432
1	59	372
2	153	372
3	277	372
4	569	372
5	925	372
6	1071	372
7	1230	372
8	1242	372
9	1242	372
10	1171	372

prune20.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	3	32

Error

0.0b

Counts

32 → 3

Alt Table

Status	Error	Program
✓	5.6b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
▶	1.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	19.4b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y z 1) 2) (.f64 z z)) x) (+.f64 z (fma.f64 y z 1)))

Compiler

Compiled 443 to 257 computations (42% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 z x)) x)
✓	0.0b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	2.6b	(.f64 y (.f64 z x))

series31.0ms (0.6%)

Counts

3 → 60

Calls

3 calls:

16.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
8.0ms	(.f64 y (.f64 z x))
7.0ms	(+.f64 (.f64 y (.f64 z x)) x)

rewrite88.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

680×	`fma-def_binary64`
532×	`log-prod_binary64`
321×	`fma-neg_binary64`
254×	`egg-rr`
178×	`expm1-udef_binary64`

Counts

3 → 254

Calls

3 calls:

82.0ms	(+.f64 (.f64 y (.f64 z x)) x)
82.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
82.0ms	(.f64 y (.f64 z x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	187	29
2	2642	29
3	5635	29
0	0	0
1	0	0

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-def_binary64`
459×	`fma-neg_binary64`
147×	`distribute-rgt-in_binary64`
135×	`unsub-neg_binary64`
110×	`distribute-lft-in_binary64`

Counts

314 → 269

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	696
1	71	528
2	173	528
3	388	528
4	809	528
5	1155	528
6	1272	528
7	1292	528
8	1292	528
9	1221	528

prune175.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	264	5	269
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	265	7	272

Error

0.0b

Counts

272 → 7

Alt Table

Status	Error	Program
✓	5.6b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	34.6b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 z x)) (-.f64 x (*.f64 z x)))
	1.6b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z x)) 2) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))
▶	1.3b	(fma.f64 z (neg.f64 x) (fma.f64 y (*.f64 z x) x))
	24.6b	(-.f64 (+.f64 (pow.f64 (sqrt.f64 (.f64 y (.f64 z x))) 2) x) (*.f64 z x))
	30.9b	(.f64 (-.f64 (.f64 y x) x) z)
	19.4b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y z 1) 2) (.f64 z z)) x) (+.f64 z (fma.f64 y z 1)))

Compiler

Compiled 5040 to 1208 computations (76% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.3b	(fma.f64 y (*.f64 z x) x)

series8.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 y (*.f64 z x) x)

rewrite44.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

526×	`log1p-expm1-u_binary64`
526×	`expm1-log1p-u_binary64`
356×	`unpow-prod-down_binary64`
297×	`log-prod_binary64`
160×	`pow2_binary64`

Counts

1 → 36

Calls

1 calls:

43.0ms

(fma.f64 y (*.f64 z x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	118	8
2	1376	8
3	5218	8
0	0	0
1	0	0

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

31×	`fma-def_binary64`
11×	`associate-r_binary64`
11×	`associate-l_binary64`
5×	`*-commutative_binary64`
5×	`*-lft-identity_binary64`

Counts

72 → 41

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	270
1	21	270
2	37	270
3	37	270
4	62	270
5	56	270
6	58	270
7	56	270

prune31.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	41	7	48

Error

0.0b

Counts

48 → 7

Alt Table

Status	Error	Program
✓	5.6b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	34.6b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 z x)) (-.f64 x (*.f64 z x)))
▶	1.6b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z x)) 2) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))
✓	1.3b	(fma.f64 z (neg.f64 x) (fma.f64 y (*.f64 z x) x))
	24.6b	(-.f64 (+.f64 (pow.f64 (sqrt.f64 (.f64 y (.f64 z x))) 2) x) (*.f64 z x))
	30.9b	(.f64 (-.f64 (.f64 y x) x) z)
	19.4b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y z 1) 2) (.f64 z z)) x) (+.f64 z (fma.f64 y z 1)))

Compiler

Compiled 865 to 303 computations (65% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z x)) 2) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))
✓	0.3b	(.f64 (cbrt.f64 (.f64 z x)) y)
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 z x)) 2)
✓	10.3b	(cbrt.f64 (*.f64 z x))

series2.4s (42.4%)

Counts

4 → 120

Calls

4 calls:

859.0ms	(.f64 (cbrt.f64 (.f64 z x)) y)
548.0ms	(pow.f64 (cbrt.f64 (*.f64 z x)) 2)
534.0ms	(cbrt.f64 (*.f64 z x))
448.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z x)) 2) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))

rewrite157.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

816×	`prod-diff_binary64`
596×	`fma-udef_binary64`
218×	`fma-neg_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`

Counts

4 → 93

Calls

4 calls:

155.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z x)) 2) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))
155.0ms	(.f64 (cbrt.f64 (.f64 z x)) y)
155.0ms	(pow.f64 (cbrt.f64 (*.f64 z x)) 2)
155.0ms	(cbrt.f64 (*.f64 z x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	51
1	234	38
2	2749	38
3	4729	38
4	4626	38
5	5082	38
0	0	0
1	0	0

simplify222.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1348×	`fma-neg_binary64`
756×	`associate-l_binary64`
656×	`associate-r_binary64`
419×	`fma-def_binary64`
327×	`times-frac_binary64`

Counts

213 → 134

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	86	2300
1	240	2300
2	449	1987
3	1106	1211
4	4228	1187
5	4085	1187
6	4865	1171
7	4967	1171
8	4996	1171
9	4999	1171
10	6101	1171

prune132.0ms (2.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	165	8	173

Error

Counts

173 → 8

Alt Table

Status	Error	Program
✓	5.6b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	34.6b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 z x)) (-.f64 x (*.f64 z x)))
✓	1.6b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z x)) 2) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))
✓	1.3b	(fma.f64 z (neg.f64 x) (fma.f64 y (*.f64 z x) x))
	24.6b	(-.f64 (+.f64 (pow.f64 (sqrt.f64 (.f64 y (.f64 z x))) 2) x) (*.f64 z x))
	30.9b	(.f64 (-.f64 (.f64 y x) x) z)
	19.4b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y z 1) 2) (.f64 z z)) x) (+.f64 z (fma.f64 y z 1)))
	1.6b	(fma.f64 (.f64 (pow.f64 (cbrt.f64 z) 2) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))

Compiler

Compiled 3413 to 1075 computations (68.5% saved)

regimes381.0ms (6.8%)

Accuracy

Total 0.2b remaining (96%)

Threshold costs 0.2b (96%)

Counts

35 → 3

Compiler

Compiled 3482 to 2114 computations (39.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`sub-neg_binary64`
10×	`+-commutative_binary64`
10×	`*-commutative_binary64`
10×	`cancel-sign-sub-inv_binary64`
7×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	80
1	49	80
2	72	80
3	89	80
4	99	80
5	101	80
6	97	80

end123.0ms (2.2%)

Compiler: Compiled 251 to 143 computations (43% saved)

Details

analyze422.0ms (7.5%)

sample1.1s (19.7%)

simplify44.0ms (0.8%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series13.0ms (0.2%)

rewrite52.0ms (0.9%)

simplify61.0ms (1.1%)

prune20.0ms (0.4%)

localize5.0ms (0.1%)

series31.0ms (0.6%)

rewrite88.0ms (1.6%)

simplify71.0ms (1.3%)

prune175.0ms (3.1%)

localize8.0ms (0.1%)

series8.0ms (0.1%)

rewrite44.0ms (0.8%)

simplify17.0ms (0.3%)

prune31.0ms (0.5%)

localize11.0ms (0.2%)

series2.4s (42.4%)

rewrite157.0ms (2.8%)

simplify222.0ms (3.9%)

prune132.0ms (2.4%)

regimes381.0ms (6.8%)

bsearch1.0ms (0%)

simplify6.0ms (0.1%)

end123.0ms (2.2%)

Profiling