Details

analyze2.2s (15.2%)

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)

sample4.0s (27.3%)

Symmetry

(sort x y)

(sort z t)

Results

2.3s	8256×	body	128	valid
1.6s	7357×	body	128	invalid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify218.0ms (1.5%)

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

5.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.6b	(.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)

localize15.0ms (0.1%)

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))
✓	7.2b	(.f64 (.f64 c (fma.f64 b c a)) i)

series98.0ms (0.7%)

Counts

4 → 228

Calls

4 calls:

57.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
21.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
10.0ms	(fma.f64 x y (*.f64 z t))
9.0ms	(*.f64 c (fma.f64 b c a))

rewrite88.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

160× egg-rr

Counts

4 → 160

Calls

2 calls:

83.0ms	((.f64 (.f64 c (fma.f64 b c a)) i) (.f64 c (fma.f64 b c a)) (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)) (fma.f64 x y (*.f64 z t)))
0.0ms	()

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

simplify392.0ms (2.7%)

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

prune205.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	191	7	198
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	191	8	199

Error

0.0b

Counts

199 → 8

Alt Table

Status	Error	Program
	5.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (pow.f64 (cbrt.f64 (.f64 c (fma.f64 c b a))) 3) i)))
	11.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	28.7b	(.f64 2 (/.f64 (-.f64 (pow.f64 (fma.f64 x y (.f64 z t)) 2) (pow.f64 (.f64 (.f64 c (fma.f64 c b a)) i) 2)) (fma.f64 (.f64 c (fma.f64 c b a)) i (fma.f64 x y (.f64 z t)))))
✓	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	19.9b	(.f64 2 (fma.f64 t z (.f64 y x)))
▶	4.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	6.7b	(.f64 2 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) 2)))
	34.1b	(.f64 2 (fma.f64 (.f64 (neg.f64 (.f64 c (fma.f64 c b a))) (sqrt.f64 i)) (sqrt.f64 i) (fma.f64 x y (.f64 z t))))

Compiler

Compiled 5978 to 1468 computations (75.4% saved)

localize12.0ms (0.1%)

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 c (*.f64 i (fma.f64 c b a))))
✓	0.8b	(*.f64 i (fma.f64 c b a))
✓	4.1b	(.f64 c (.f64 i (fma.f64 c b a)))

series95.0ms (0.6%)

Counts

3 → 192

Calls

3 calls:

60.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (*.f64 i (fma.f64 c b a))))
24.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
11.0ms	(*.f64 i (fma.f64 c b a))

rewrite87.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

143× egg-rr

Counts

3 → 143

Calls

2 calls:

83.0ms	((.f64 c (.f64 i (fma.f64 c b a))) (.f64 i (fma.f64 c b a)) (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	311	40
2	3879	40
3	5298	40
0	0	0
1	0	0

simplify366.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

335 → 182

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	51	3283
1	121	2587
2	279	2587
3	568	2587
4	1776	2587
5	2670	2587
6	3267	2587
7	3703	2587
8	4161	2587
9	4249	2587
10	4344	2435
11	3348	2435
12	3490	2435
13	4121	2435
14	4413	2435
15	4569	2435
16	4846	2435
17	4912	2435

prune199.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	207	6	213

Error

Counts

213 → 6

Alt Table

Status	Error	Program
	19.9b	(.f64 2 (fma.f64 t z (.f64 y x)))
	4.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (pow.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) 3))))
✓	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	6.7b	(.f64 2 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) 2)))
▶	2.3b	(.f64 2 (fma.f64 (.f64 c i) (neg.f64 (fma.f64 c b a)) (fma.f64 x y (*.f64 z t))))
	7.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))

Compiler

Compiled 5980 to 1396 computations (76.7% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (*.f64 z t))
✓	2.2b	(fma.f64 (.f64 c i) (neg.f64 (fma.f64 c b a)) (fma.f64 x y (.f64 z t)))

series60.0ms (0.4%)

Counts

1 → 96

Calls

1 calls:

60.0ms

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

rewrite112.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

24× egg-rr

Counts

1 → 24

Calls

2 calls:

111.0ms	((fma.f64 (.f64 c i) (neg.f64 (fma.f64 c b a)) (fma.f64 x y (.f64 z t))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	298	19
2	3303	19
3	4824	19
4	4991	19
5	4961	19
0	0	0
1	0	0

simplify277.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1019×	`distribute-rgt-neg-in_binary64`
917×	`fma-neg_binary64`
702×	`fabs-mul_binary64`
648×	`distribute-lft-neg-in_binary64`
638×	`cancel-sign-sub-inv_binary64`

Counts

120 → 47

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	39	2199
1	98	1968
2	246	1891
3	526	1737
4	1663	1737
5	2554	1737
6	3170	1737
7	3619	1737
8	4077	1737
9	4162	1737
10	4259	1565
11	3323	1565
12	3242	1565
13	3757	1565
14	4486	1565
15	4839	1565

prune53.0ms (0.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	70	6	76

Error

Counts

76 → 6

Alt Table

Status	Error	Program
	19.9b	(.f64 2 (fma.f64 t z (.f64 y x)))
▶	4.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (pow.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) 3))))
✓	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	6.7b	(.f64 2 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) 2)))
✓	2.3b	(.f64 2 (fma.f64 (.f64 c i) (neg.f64 (fma.f64 c b a)) (fma.f64 x y (*.f64 z t))))
	7.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))

Compiler

Compiled 1677 to 555 computations (66.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 i (fma.f64 c b a))) 3)
	0.8b	(*.f64 i (fma.f64 c b a))
✓	4.1b	(.f64 c (pow.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) 3))
✓	7.8b	(cbrt.f64 (*.f64 i (fma.f64 c b a)))

series3.1s (20.8%)

Counts

3 → 144

Calls

3 calls:

2.7s	(pow.f64 (cbrt.f64 (*.f64 i (fma.f64 c b a))) 3)
357.0ms	(cbrt.f64 (*.f64 i (fma.f64 c b a)))
32.0ms	(.f64 c (pow.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) 3))

rewrite142.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

76× egg-rr

Counts

3 → 76

Calls

2 calls:

141.0ms	((cbrt.f64 (.f64 i (fma.f64 c b a))) (.f64 c (pow.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) 3)) (pow.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) 3))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	206	29
2	2311	29
3	5439	29
0	0	0
1	0	0

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
311×	`unswap-sqr_binary64`
279×	`associate-r_binary64`
236×	`times-frac_binary64`
207×	`associate-/l*_binary64`

Counts

220 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	5006
1	974	4513
2	3347	4270
3	4987	4270

prune197.0ms (1.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	213	6	219

Error

Counts

219 → 6

Alt Table

Status	Error	Program
	19.9b	(.f64 2 (fma.f64 t z (.f64 y x)))
✓	4.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (pow.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) 3))))
✓	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	6.7b	(.f64 2 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 c b a)) i))) 2)))
✓	2.3b	(.f64 2 (fma.f64 (.f64 c i) (neg.f64 (fma.f64 c b a)) (fma.f64 x y (*.f64 z t))))
	7.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))

Compiler

Compiled 7591 to 3581 computations (52.8% saved)

regimes2.4s (16.7%)

Accuracy

Total 1.1b remaining (97.1%)

Threshold costs 0b (0%)

Counts

113 → 3

Compiler

Compiled 46417 to 30590 computations (34.1% saved)

bsearch4.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
14×	`+-commutative_binary64`
12×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	113
1	67	113
2	81	113
3	93	113
4	114	113
5	130	113
6	140	113
7	145	113
8	146	113
9	146	113

end147.0ms (1%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 683 to 329 computations (51.8% saved)

Iter	Nodes	Cost
0	39	113
1	67	113
2	81	113
3	93	113
4	114	113
5	130	113
6	140	113
7	145	113
8	146	113
9	146	113

Iter	Nodes	Cost
0	39	113
1	67	113
2	81	113
3	93	113
4	114	113
5	130	113
6	140	113
7	145	113
8	146	113
9	146	113

Details

analyze2.2s (15.2%)

sample4.0s (27.3%)

simplify218.0ms (1.5%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series98.0ms (0.7%)

rewrite88.0ms (0.6%)

simplify392.0ms (2.7%)

prune205.0ms (1.4%)

localize12.0ms (0.1%)

series95.0ms (0.6%)

rewrite87.0ms (0.6%)

simplify366.0ms (2.5%)

prune199.0ms (1.4%)

localize12.0ms (0.1%)

series60.0ms (0.4%)

rewrite112.0ms (0.8%)

simplify277.0ms (1.9%)

prune53.0ms (0.4%)

localize15.0ms (0.1%)

series3.1s (20.8%)

rewrite142.0ms (1%)

simplify119.0ms (0.8%)

prune197.0ms (1.3%)

regimes2.4s (16.7%)

bsearch4.0ms (0%)

simplify7.0ms (0%)

end147.0ms (1%)

Profiling

Iter	Nodes	Cost
0	39	113
1	67	113
2	81	113
3	93	113
4	114	113
5	130	113
6	140	113
7	145	113
8	146	113
9	146	113