Details

analyze2.6s (24.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 28 to 19 computations (32.1% saved)

sample3.2s (30%)

Symmetry

(sort x y)

(sort z t)

Results

1.7s	8256×	body	128	valid
1.4s	7495×	body	128	invalid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify219.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1133×	`distribute-rgt-in_binary64`
1066×	`distribute-lft-in_binary64`
969×	`unsub-neg_binary64`
583×	`fma-def_binary64`
461×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	37	24
2	97	24
3	277	24
4	797	24
5	1809	24
6	2532	24
7	2783	24
8	3128	24
9	3409	24
10	3319	24
11	3327	24
12	3331	24
13	3461	24
14	3620	24
15	3621	24
16	3623	24
17	3623	24
18	5071	24

prune4.0ms (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

6.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 94 to 57 computations (39.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
✓	0.1b	(*.f64 c (fma.f64 b c a))
✓	8.6b	(.f64 (.f64 c (fma.f64 b c a)) i)

series93.0ms (0.9%)

Counts

4 → 228

Calls

4 calls:

55.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
20.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
11.0ms	(*.f64 c (fma.f64 b c a))
8.0ms	(fma.f64 x y (*.f64 z t))

rewrite99.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

367×	`fma-def_binary64`
294×	`expm1-udef_binary64`
294×	`log1p-udef_binary64`
174×	`fma-neg_binary64`
163×	`add-sqr-sqrt_binary64`

Counts

4 → 160

Calls

4 calls:

94.0ms	(fma.f64 x y (*.f64 z t))
94.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
94.0ms	(*.f64 c (fma.f64 b c a))
94.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	311	48
2	3872	48
3	5289	48
0	0	0
1	0	0

simplify451.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
891×	`distribute-rgt-neg-in_binary64`
739×	`cube-prod_binary64`
707×	`distribute-lft-neg-in_binary64`
670×	`fabs-mul_binary64`

Counts

388 → 198

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	47	3604
1	113	2908
2	275	2827
3	572	2827
4	1777	2827
5	2670	2827
6	3267	2827
7	3703	2827
8	4161	2827
9	4249	2827
10	4344	2675
11	3348	2675
12	3490	2675
13	4121	2675
14	4413	2675
15	4569	2675
16	4846	2675
17	4912	2675

prune181.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	193	5	198
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	193	6	199

Error

0.0b

Counts

199 → 6

Alt Table

Status	Error	Program
	29.4b	(.f64 2 (-.f64 (.f64 t z) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
▶	5.3b	(.f64 2 (fma.f64 c (neg.f64 (.f64 (fma.f64 c b a) i)) (fma.f64 x y (*.f64 z t))))
	36.8b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) 2))
	22.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)))
	32.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (pow.f64 (sqrt.f64 (.f64 c (fma.f64 c b a))) 2) i)))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 5816 to 1398 computations (76% saved)

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (*.f64 z t))
✓	1.0b	(*.f64 (fma.f64 c b a) i)
✓	4.1b	(fma.f64 c (neg.f64 (.f64 (fma.f64 c b a) i)) (fma.f64 x y (.f64 z t)))

series81.0ms (0.8%)

Counts

2 → 144

Calls

2 calls:

71.0ms	(fma.f64 c (neg.f64 (.f64 (fma.f64 c b a) i)) (fma.f64 x y (.f64 z t)))
10.0ms	(*.f64 (fma.f64 c b a) i)

rewrite147.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

319×	`prod-diff_binary64`
267×	`expm1-udef_binary64`
267×	`log1p-udef_binary64`
215×	`fma-neg_binary64`
210×	`fma-udef_binary64`

Counts

2 → 48

Calls

2 calls:

146.0ms	(*.f64 (fma.f64 c b a) i)
146.0ms	(fma.f64 c (neg.f64 (.f64 (fma.f64 c b a) i)) (fma.f64 x y (.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	302	27
2	3394	27
3	4908	27
4	4978	27
5	5041	27
0	0	0
1	0	0

simplify330.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1017×	`distribute-rgt-neg-in_binary64`
913×	`fma-neg_binary64`
702×	`fabs-mul_binary64`
646×	`distribute-lft-neg-in_binary64`
635×	`cube-prod_binary64`

Counts

192 → 80

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	47	2679
1	118	2331
2	271	2100
3	542	2100
4	1665	2100
5	2554	2100
6	3170	2100
7	3619	2100
8	4077	2100
9	4162	2100
10	4259	1928
11	3323	1928
12	3242	1928
13	3757	1928
14	4486	1928
15	4839	1928

prune97.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	102	7	109

Error

0.0b

Counts

109 → 7

Alt Table

Status	Error	Program
	29.4b	(.f64 2 (-.f64 (.f64 t z) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
▶	6.8b	(.f64 2 (fma.f64 c (neg.f64 (+.f64 (.f64 c (.f64 i b)) (.f64 a i))) (fma.f64 x y (*.f64 z t))))
✓	5.3b	(.f64 2 (fma.f64 c (neg.f64 (.f64 (fma.f64 c b a) i)) (fma.f64 x y (*.f64 z t))))
	36.8b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) 2))
	22.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)))
	32.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (pow.f64 (sqrt.f64 (.f64 c (fma.f64 c b a))) 2) i)))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 2382 to 823 computations (65.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(+.f64 (.f64 c (.f64 i b)) (*.f64 a i))
✓	4.1b	(fma.f64 c (neg.f64 (+.f64 (.f64 c (.f64 i b)) (.f64 a i))) (fma.f64 x y (.f64 z t)))
✓	5.4b	(.f64 c (.f64 i b))

series114.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

67.0ms	(fma.f64 c (neg.f64 (+.f64 (.f64 c (.f64 i b)) (.f64 a i))) (fma.f64 x y (.f64 z t)))
31.0ms	(.f64 c (.f64 i b))
16.0ms	(+.f64 (.f64 c (.f64 i b)) (*.f64 a i))

rewrite79.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

316×	`expm1-udef_binary64`
316×	`log1p-udef_binary64`
184×	`add-sqr-sqrt_binary64`
170×	`log1p-expm1-u_binary64`
170×	`expm1-log1p-u_binary64`

Counts

3 → 97

Calls

3 calls:

74.0ms	(+.f64 (.f64 c (.f64 i b)) (*.f64 a i))
74.0ms	(fma.f64 c (neg.f64 (+.f64 (.f64 c (.f64 i b)) (.f64 a i))) (fma.f64 x y (.f64 z t)))
74.0ms	(.f64 c (.f64 i b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	354	40
2	4251	40
3	5146	40
0	0	0
1	0	0

simplify305.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1017×	`distribute-rgt-neg-in_binary64`
913×	`fma-neg_binary64`
702×	`fabs-mul_binary64`
646×	`distribute-lft-neg-in_binary64`
635×	`cube-prod_binary64`

Counts

229 → 126

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	45	2547
1	116	2235
2	270	2004
3	541	2004
4	1664	2004
5	2554	2004
6	3170	2004
7	3619	2004
8	4077	2004
9	4162	2004
10	4259	1832
11	3323	1832
12	3242	1832
13	3757	1832
14	4486	1832
15	4839	1832

prune152.0ms (1.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	149	7	156

Error

0.0b

Counts

156 → 7

Alt Table

Status	Error	Program
	29.4b	(.f64 2 (-.f64 (.f64 t z) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
✓	6.8b	(.f64 2 (fma.f64 c (neg.f64 (+.f64 (.f64 c (.f64 i b)) (.f64 a i))) (fma.f64 x y (*.f64 z t))))
✓	5.3b	(.f64 2 (fma.f64 c (neg.f64 (.f64 (fma.f64 c b a) i)) (fma.f64 x y (*.f64 z t))))
	36.8b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) 2))
▶	22.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)))
	32.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (pow.f64 (sqrt.f64 (.f64 c (fma.f64 c b a))) 2) i)))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 4023 to 1222 computations (69.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 c (fma.f64 c b a))
✓	0.2b	(pow.f64 (*.f64 c (fma.f64 c b a)) 3)
✓	8.6b	(.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)
✓	26.1b	(cbrt.f64 (pow.f64 (*.f64 c (fma.f64 c b a)) 3))

series94.0ms (0.9%)

Counts

4 → 156

Calls

4 calls:

34.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)
27.0ms	(pow.f64 (*.f64 c (fma.f64 c b a)) 3)
22.0ms	(cbrt.f64 (pow.f64 (*.f64 c (fma.f64 c b a)) 3))
11.0ms	(*.f64 c (fma.f64 c b a))

rewrite59.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

885×	`log1p-expm1-u_binary64`
885×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
94×	`add-cbrt-cube_binary64`
93×	`add-log-exp_binary64`

Counts

4 → 92

Calls

4 calls:

57.0ms	(*.f64 c (fma.f64 c b a))
57.0ms	(pow.f64 (*.f64 c (fma.f64 c b a)) 3)
57.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)
57.0ms	(cbrt.f64 (pow.f64 (*.f64 c (fma.f64 c b a)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	207	38
2	2321	38
3	5461	38
0	0	0
1	0	0

simplify135.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-neg_binary64`
598×	`unswap-sqr_binary64`
442×	`associate-l_binary64`
410×	`fma-def_binary64`
365×	`associate-r_binary64`

Counts

248 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	2693
1	196	2477
2	568	2186
3	2130	2132
4	4314	2132
5	4968	2132
6	4960	2132

prune176.0ms (1.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	112	7	119

Error

0.0b

Counts

119 → 7

Alt Table

Status	Error	Program
	29.4b	(.f64 2 (-.f64 (.f64 t z) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
✓	6.8b	(.f64 2 (fma.f64 c (neg.f64 (+.f64 (.f64 c (.f64 i b)) (.f64 a i))) (fma.f64 x y (*.f64 z t))))
✓	5.3b	(.f64 2 (fma.f64 c (neg.f64 (.f64 (fma.f64 c b a) i)) (fma.f64 x y (*.f64 z t))))
	36.8b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) 2))
✓	22.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)))
	32.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (pow.f64 (sqrt.f64 (.f64 c (fma.f64 c b a))) 2) i)))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 2856 to 1169 computations (59.1% saved)

regimes1.8s (16.8%)

Accuracy

Total 0.3b remaining (85.1%)

Threshold costs 0.3b (85.1%)

Counts

60 → 3

Compiler

Compiled 22612 to 15358 computations (32.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	108
1	52	108
2	68	108
3	79	108
4	87	108
5	90	108
6	90	108

end193.0ms (1.8%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 687 to 330 computations (52% saved)

Details

analyze2.6s (24.2%)

sample3.2s (30%)

simplify219.0ms (2.1%)

prune4.0ms (0%)

localize18.0ms (0.2%)

series93.0ms (0.9%)

rewrite99.0ms (0.9%)

simplify451.0ms (4.2%)

prune181.0ms (1.7%)

localize20.0ms (0.2%)

series81.0ms (0.8%)

rewrite147.0ms (1.4%)

simplify330.0ms (3.1%)

prune97.0ms (0.9%)

localize16.0ms (0.2%)

series114.0ms (1.1%)

rewrite79.0ms (0.7%)

simplify305.0ms (2.9%)

prune152.0ms (1.4%)

localize17.0ms (0.2%)

series94.0ms (0.9%)

rewrite59.0ms (0.6%)

simplify135.0ms (1.3%)

prune176.0ms (1.7%)

regimes1.8s (16.8%)

bsearch2.0ms (0%)

simplify9.0ms (0.1%)

end193.0ms (1.8%)

Profiling