Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample9.5s (84.5%)

Results

7.6s	4107×	body	2048	valid
1.2s	2106×	body	1024	valid
317.0ms	1028×	body	512	valid
204.0ms	240×	body	4096	valid
110.0ms	531×	body	256	valid
31.0ms	244×	body	128	valid

Compiler

Compiled 41 to 31 computations (24.4% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

prune2.0ms (0%)

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

60.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	60.1b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series24.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(/.f64 1 (tan.f64 x))
10.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite61.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

823×	`log1p-expm1-u_binary64`
823×	`expm1-log1p-u_binary64`
592×	`prod-diff_binary64`
126×	`egg-rr`
82×	`add-sqr-sqrt_binary64`

Counts

2 → 126

Calls

2 calls:

58.0ms	(/.f64 1 (tan.f64 x))
58.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	160	18
2	2070	18
3	6169	18
0	0	0
1	0	0

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
529×	`distribute-rgt-neg-in_binary64`
519×	`associate-l_binary64`
498×	`cancel-sign-sub-inv_binary64`
420×	`distribute-lft-neg-in_binary64`

Counts

150 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	281
1	88	281
2	215	279
3	524	275
4	1318	275
5	2674	275
6	3921	275
7	4461	275
8	4870	275

prune73.0ms (0.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	1	145

Error

0.4b

Counts

145 → 1

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))))

Compiler

Compiled 2955 to 1813 computations (38.6% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.4b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

series6.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
3.0ms	(*.f64 1/45 (pow.f64 x 3))

rewrite43.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

649×	`log1p-expm1-u_binary64`
649×	`expm1-log1p-u_binary64`
305×	`log-prod_binary64`
134×	`expm1-udef_binary64`
134×	`log1p-udef_binary64`

Counts

2 → 45

Calls

2 calls:

42.0ms	(*.f64 1/45 (pow.f64 x 3))
42.0ms	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	167	18
2	1695	18
3	5117	18
0	0	0
1	0	0

simplify149.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
529×	`cube-prod_binary64`
522×	`pow-sqr_binary64`
481×	`fabs-mul_binary64`
452×	`associate-l_binary64`

Counts

57 → 48

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	117
1	22	117
2	41	117
3	70	117
4	118	117
5	246	117
6	679	117
7	996	117
8	1000	117
9	1130	117
10	1284	117
11	1438	117
12	1667	117
13	1968	117
14	2316	117
15	2791	117
16	3409	117
17	3605	117
18	3779	117
19	3893	117
20	3940	117
21	3992	117
22	4870	117
23	4773	117

prune56.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Error

0.2b

Counts

49 → 6

Alt Table

Status	Error	Program
	30.8b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (pow.f64 (sqrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)))
▶	1.5b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)))
	28.2b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (/.f64 (-.f64 (.f64 (.f64 1/3 x) (.f64 1/3 x)) (.f64 1/2025 (pow.f64 x 6))) (-.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3))))))
	41.7b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (/.f64 (+.f64 (pow.f64 (.f64 1/3 x) 3) (pow.f64 (.f64 1/45 (pow.f64 x 3)) 3)) (fma.f64 (.f64 1/3 x) (.f64 1/3 x) (-.f64 (.f64 1/2025 (pow.f64 x 6)) (.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3))))))))
✓	0.4b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))))
	1.6b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2))))

Compiler

Compiled 1444 to 1167 computations (19.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/45 (pow.f64 x 3))
	0.4b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
✓	0.6b	(cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)

series76.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

68.0ms	(pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)
7.0ms	(cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))

rewrite43.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

722×	`log1p-expm1-u_binary64`
722×	`expm1-log1p-u_binary64`
146×	`expm1-udef_binary64`
146×	`log1p-udef_binary64`
117×	`prod-diff_binary64`

Counts

2 → 49

Calls

2 calls:

42.0ms	(cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))
42.0ms	(pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	190	24
2	1895	24
3	4942	24
0	0	0
1	0	0

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

383×	`fma-neg_binary64`
370×	`cancel-sign-sub-inv_binary64`
292×	`unswap-sqr_binary64`
232×	`fma-def_binary64`
209×	`associate-/l/_binary64`

Counts

73 → 85

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	84	1184
1	238	1134
2	629	827
3	2353	524
4	4638	508
5	4994	508
6	4939	508

prune134.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	133	6	139

Error

0.2b

Counts

139 → 6

Alt Table

Status	Error	Program
	41.8b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (+.f64 (/.f64 15 (.f64 x x)) 1) (*.f64 1/45 (pow.f64 x 3)))))
	1.9b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)) 3)))
	30.8b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (pow.f64 (sqrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)))
	41.7b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (/.f64 (+.f64 (pow.f64 (.f64 1/3 x) 3) (pow.f64 (.f64 1/45 (pow.f64 x 3)) 3)) (fma.f64 (.f64 1/3 x) (.f64 1/3 x) (-.f64 (.f64 1/2025 (pow.f64 x 6)) (.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3))))))))
✓	0.4b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))))
▶	1.6b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2))))

Compiler

Compiled 4153 to 3425 computations (17.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2))
	0.4b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)
	0.6b	(cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))))

series19.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

16.0ms	(pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)
3.0ms	(.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2))

rewrite46.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

813×	`log1p-expm1-u_binary64`
813×	`expm1-log1p-u_binary64`
117×	`prod-diff_binary64`
101×	`add-sqr-sqrt_binary64`
97×	`add-cbrt-cube_binary64`

Counts

2 → 37

Calls

2 calls:

45.0ms	(.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2))
45.0ms	(pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	228	25
2	2143	25
3	5035	25
0	0	0
1	0	0

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-neg_binary64`
545×	`cancel-sign-sub-inv_binary64`
298×	`neg-mul-1_binary64`
264×	`distribute-rgt-neg-in_binary64`
258×	`associate-r_binary64`

Counts

61 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	79	893
1	221	863
2	604	623
3	2663	481
4	4451	469
5	4894	469
6	4919	469

prune245.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	214	11	225

Error

0.1b

Counts

225 → 11

Alt Table

Status	Error	Program
	1.9b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)) 2))))
	41.7b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (/.f64 (+.f64 (pow.f64 (.f64 1/3 x) 3) (pow.f64 (.f64 1/45 (pow.f64 x 3)) 3)) (fma.f64 (.f64 1/3 x) (.f64 1/3 x) (-.f64 (.f64 1/2025 (pow.f64 x 6)) (.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3))))))))
	31.3b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)) 2))))
✓	0.4b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))))
	2.0b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))))) 3) (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2))))
	32.7b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (exp.f64 (log.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))))) (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2))))
	28.5b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 2)))))
	32.7b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (.f64 (cbrt.f64 (pow.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))) 2/3)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))))) (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))))))))
	41.8b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 (+.f64 (/.f64 15 (.f64 x x)) 1) (*.f64 1/45 (pow.f64 x 3)))))
	1.9b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)) 3)))
	30.8b	(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (pow.f64 (sqrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)))

Compiler

Compiled 9024 to 7415 computations (17.8% saved)

regimes175.0ms (1.5%)

Accuracy

Total 0.2b remaining (45.3%)

Threshold costs 0.2b (45.3%)

Counts

76 → 1

Compiler

Compiled 4094 to 3378 computations (17.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	17	25
2	17	25

end286.0ms (2.5%)

Compiler: Compiled 399 to 325 computations (18.5% saved)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

Details

analyze5.0ms (0%)

sample9.5s (84.5%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series24.0ms (0.2%)

rewrite61.0ms (0.5%)

simplify85.0ms (0.8%)

prune73.0ms (0.6%)

localize10.0ms (0.1%)

series6.0ms (0.1%)

rewrite43.0ms (0.4%)

simplify149.0ms (1.3%)

prune56.0ms (0.5%)

localize14.0ms (0.1%)

series76.0ms (0.7%)

rewrite43.0ms (0.4%)

simplify80.0ms (0.7%)

prune134.0ms (1.2%)

localize14.0ms (0.1%)

series19.0ms (0.2%)

rewrite46.0ms (0.4%)

simplify83.0ms (0.7%)

prune245.0ms (2.2%)

regimes175.0ms (1.5%)

simplify2.0ms (0%)

end286.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12