Details

analyze9.0ms (0.1%)

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)

sample9.7s (88.3%)

Results

7.6s	4106×	body	2048	valid
1.4s	2143×	body	1024	valid
335.0ms	1008×	body	512	valid
204.0ms	220×	body	4096	valid
121.0ms	536×	body	256	valid
32.0ms	243×	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

59.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	59.9b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.4b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series12.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

12.0ms

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

rewrite62.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

1 → 103

Calls

1 calls:

55.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	160	12
2	2070	12
3	6169	12
0	0	0
1	0	0

simplify155.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1116×	`sqr-pow_binary64`
672×	`cube-prod_binary64`
636×	`fabs-mul_binary64`
624×	`unswap-sqr_binary64`
556×	`fma-def_binary64`

Counts

115 → 113

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	162
1	69	162
2	145	162
3	307	162
4	523	162
5	997	162
6	1399	162
7	1943	162
8	2123	162
9	2375	162
10	2677	162
11	3075	162
12	3449	162
13	3956	162
14	4178	162
15	4311	162
16	4509	162
17	4626	162
18	4752	162
19	5438	162

prune57.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Error

0.3b

Counts

114 → 2

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
▶	0.3b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

Compiler

Compiled 2596 to 1575 computations (39.3% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.3b	(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))

rewrite41.0ms (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 → 47

Calls

2 calls:

40.0ms	(*.f64 1/45 (pow.f64 x 3))
40.0ms	(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

simplify147.0ms (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

59 → 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

prune47.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	42	8	50

Error

0.2b

Counts

50 → 8

Alt Table

Status	Error	Program
	1.5b	(.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))
✓	0.3b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
	38.0b	(cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3))
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)
	1.5b	(pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)
	28.8b	(/.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))))
	40.1b	(/.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	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))

Compiler

Compiled 910 to 741 computations (18.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.1b	(*.f64 2/945 (pow.f64 x 5))
✓	0.4b	(*.f64 1/3 x)

series11.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

8.0ms	(*.f64 1/3 x)
3.0ms	(*.f64 2/945 (pow.f64 x 5))

rewrite41.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

654×	`log1p-expm1-u_binary64`
654×	`expm1-log1p-u_binary64`
322×	`log-prod_binary64`
138×	`expm1-udef_binary64`
138×	`log1p-udef_binary64`

Counts

2 → 34

Calls

2 calls:

41.0ms	(*.f64 2/945 (pow.f64 x 5))
41.0ms	(*.f64 1/3 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	168	11
2	1724	11
3	4923	11
0	0	0
1	0	0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune59.0ms (0.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	49	9	58

Error

0.2b

Counts

58 → 9

Alt Table

Status	Error	Program
▶	1.5b	(.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))
	45.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (sqrt.f64 (.f64 1/9 (.f64 x x)))))
✓	0.3b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
	38.0b	(cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3))
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)
	1.5b	(pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)
	28.8b	(/.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))))
	40.1b	(/.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	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))

Compiler

Compiled 1256 to 1039 computations (17.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series26.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

15.0ms

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

8.0ms

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

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))

rewrite48.0ms (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

3 → 62

Calls

3 calls:

47.0ms

(*.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))

47.0ms

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

46.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	228	40
2	2143	40
3	5035	40
0	0	0
1	0	0

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-neg_binary64`
424×	`fma-def_binary64`
339×	`associate-r_binary64`
328×	`times-frac_binary64`
290×	`associate-l_binary64`

Counts

98 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	1577
1	332	1517
2	891	1091
3	3859	951
4	4876	887
5	4936	887

prune193.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	222	2	224
Fresh	0	6	6
Picked	0	1	1
Done	1	1	2
Total	223	10	233

Error

0.2b

Counts

233 → 10

Alt Table

Status	Error	Program
	1.5b	(pow.f64 (cbrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 3)
	2.0b	(.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))))) 2) (.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)))))))
✓	1.5b	(.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))
	45.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (sqrt.f64 (.f64 1/9 (.f64 x x)))))
✓	0.3b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
	35.5b	(.f64 (cbrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) (pow.f64 (cbrt.f64 (exp.f64 (log.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))))) 2))
	38.0b	(cbrt.f64 (pow.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3))) 3))
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))) 2)
	28.8b	(/.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))))
	40.1b	(/.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))))))

Compiler

Compiled 6881 to 5681 computations (17.4% saved)

regimes60.0ms (0.5%)

Accuracy

Total 0.2b remaining (40.6%)

Threshold costs 0.2b (40.6%)

Counts

27 → 1

Compiler

Compiled 1264 to 1038 computations (17.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11
2	9	11

end184.0ms (1.7%)

Compiler: Compiled 233 to 189 computations (18.9% 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

analyze9.0ms (0.1%)

sample9.7s (88.3%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize4.0ms (0%)

series12.0ms (0.1%)

rewrite62.0ms (0.6%)

simplify155.0ms (1.4%)

prune57.0ms (0.5%)

localize4.0ms (0%)

series6.0ms (0.1%)

rewrite41.0ms (0.4%)

simplify147.0ms (1.3%)

prune47.0ms (0.4%)

localize8.0ms (0.1%)

series11.0ms (0.1%)

rewrite41.0ms (0.4%)

simplify6.0ms (0.1%)

prune59.0ms (0.5%)

localize8.0ms (0.1%)

series26.0ms (0.2%)

rewrite48.0ms (0.4%)

simplify80.0ms (0.7%)

prune193.0ms (1.8%)

regimes60.0ms (0.5%)

simplify2.0ms (0%)

end184.0ms (1.7%)

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