Details

analyze5.0ms (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)

sample8.9s (87.4%)

Results

6.9s	4119×	body	2048	valid
1.2s	2107×	body	1024	valid
311.0ms	1026×	body	512	valid
192.0ms	225×	body	4096	valid
110.0ms	539×	body	256	valid
28.0ms	240×	body	128	valid

Compiler

Compiled 41 to 31 computations (24.4% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	169	12
9	205	12
10	231	12
11	233	12

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

59.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.6b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 35 to 26 computations (25.7% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (tan.f64 x))
✓	3.3b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series26.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(/.f64 1 (tan.f64 x))
12.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite49.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

823×	`expm1-log1p-u_binary64`
592×	`prod-diff_binary64`
126×	`egg-rr`
82×	`add-sqr-sqrt_binary64`
78×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	161	18
2	2343	18

Stop Event

1×	node limit

Counts

2 → 126

Calls

2 calls:

47.0ms	(/.f64 1 (tan.f64 x))
47.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

simplify35.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
496×	`cancel-sign-sub-inv_binary64`
490×	`associate-l_binary64`
352×	`fma-def_binary64`
351×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	281
1	93	281
2	228	279
3	671	275
4	1792	275
5	4640	275

Stop Event

1×	node limit

Counts

150 → 144

prune72.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	3	145

Error

0.3b

Counts

145 → 3

Alt Table

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

Compiler

Compiled 2995 to 1869 computations (37.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
✓	0.1b	(*.f64 2/945 (pow.f64 x 5))
✓	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.3b	(*.f64 1/3 x)

series10.0ms (0.1%)

Counts

4 → 9

Calls

4 calls:

3.0ms	(*.f64 2/945 (pow.f64 x 5))
3.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
3.0ms	(*.f64 1/45 (pow.f64 x 3))
2.0ms	(*.f64 1/3 x)

rewrite54.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`log-prod_binary64`
318×	`fma-def_binary64`
229×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
190×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	284	29
2	3289	29

Stop Event

1×	node limit

Counts

4 → 107

Calls

4 calls:

52.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
52.0ms	(*.f64 2/945 (pow.f64 x 5))
52.0ms	(*.f64 1/45 (pow.f64 x 3))
52.0ms	(*.f64 1/3 x)

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

732×	`sqr-pow_binary64`
441×	`associate-l_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	84
1	21	84
2	41	84
3	85	84
4	152	84
5	377	84
6	1219	84
7	1922	84
8	2009	84
9	2142	84
10	2300	84
11	2532	84
12	2854	84
13	3275	84
14	3775	84
15	4370	84

Stop Event

1×	node limit

Counts

116 → 111

prune124.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	104	10	114

Error

0.1b

Counts

114 → 10

Alt Table

Status	Error	Program
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (cbrt.f64 (.f64 1/3 x)) (pow.f64 (cbrt.f64 (.f64 1/3 x)) 2) (.f64 1/45 (pow.f64 x 3))))
	43.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (/.f64 1 (/.f64 (fma.f64 (.f64 1/3 x) (-.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3))) (.f64 1/2025 (pow.f64 x 6))) (fma.f64 (pow.f64 x 3) 1/27 (.f64 1/91125 (pow.f64 (pow.f64 x 3) 3))))))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/3) (*.f64 1/45 (pow.f64 x 3))))
	30.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (.f64 (-.f64 (.f64 1/2025 (pow.f64 x 6)) (.f64 (.f64 x x) 1/9)) (/.f64 1 (fma.f64 1/45 (pow.f64 x 3) (.f64 -1/3 x)))))
▶	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))))
	33.7b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (pow.f64 (sqrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) 2))
	30.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (/.f64 (-.f64 (.f64 1/2025 (pow.f64 x 6)) (.f64 (.f64 x x) 1/9)) (fma.f64 1/45 (pow.f64 x 3) (*.f64 -1/3 x))))
	33.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/3) (*.f64 1/45 (pow.f64 x 3))))
	43.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (.f64 (fma.f64 (pow.f64 x 3) 1/27 (.f64 1/91125 (pow.f64 (pow.f64 x 3) 3))) (/.f64 1 (fma.f64 (.f64 1/3 x) (-.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3))) (*.f64 1/2025 (pow.f64 x 6))))))
	46.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (sqrt.f64 (.f64 (.f64 x x) 1/9))))

Compiler

Compiled 2718 to 2189 computations (19.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 2/945 (pow.f64 x 5))
	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.3b	(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))

series3.0ms (0%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite35.0ms (0.3%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	167	11
2	1781	11

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

34.0ms

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

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

731×	`sqr-pow_binary64`
441×	`associate-l_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	117
1	22	117
2	41	117
3	85	117
4	152	117
5	374	117
6	1226	117
7	1931	117
8	2018	117
9	2151	117
10	2309	117
11	2541	117
12	2863	117
13	3284	117
14	3784	117
15	4379	117

Stop Event

1×	node limit

Counts

41 → 32

prune76.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	64	10	74

Error

0.1b

Counts

74 → 10

Alt Table

Status	Error	Program
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (cbrt.f64 (.f64 1/3 x)) (pow.f64 (cbrt.f64 (.f64 1/3 x)) 2) (.f64 1/45 (pow.f64 x 3))))
	43.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (/.f64 1 (/.f64 (fma.f64 (.f64 1/3 x) (-.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3))) (.f64 1/2025 (pow.f64 x 6))) (fma.f64 (pow.f64 x 3) 1/27 (.f64 1/91125 (pow.f64 (pow.f64 x 3) 3))))))
▶	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/3) (*.f64 1/45 (pow.f64 x 3))))
	30.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (.f64 (-.f64 (.f64 1/2025 (pow.f64 x 6)) (.f64 (.f64 x x) 1/9)) (/.f64 1 (fma.f64 1/45 (pow.f64 x 3) (.f64 -1/3 x)))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))))
	33.7b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (pow.f64 (sqrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) 2))
	30.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (/.f64 (-.f64 (.f64 1/2025 (pow.f64 x 6)) (.f64 (.f64 x x) 1/9)) (fma.f64 1/45 (pow.f64 x 3) (*.f64 -1/3 x))))
	33.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/3) (*.f64 1/45 (pow.f64 x 3))))
	43.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (.f64 (fma.f64 (pow.f64 x 3) 1/27 (.f64 1/91125 (pow.f64 (pow.f64 x 3) 3))) (/.f64 1 (fma.f64 (.f64 1/3 x) (-.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3))) (*.f64 1/2025 (pow.f64 x 6))))))
	46.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (sqrt.f64 (.f64 (.f64 x x) 1/9))))

Compiler

Compiled 1700 to 1383 computations (18.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series65.0ms (0.6%)

Counts

4 → 3

Calls

4 calls:

22.0ms	(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/3) (.f64 1/45 (pow.f64 x 3)))
22.0ms	(pow.f64 (cbrt.f64 x) 2)
12.0ms	(*.f64 (cbrt.f64 x) 1/3)
9.0ms	(cbrt.f64 x)

rewrite46.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

900×	`log1p-expm1-u_binary64`
900×	`expm1-log1p-u_binary64`
182×	`prod-diff_binary64`
110×	`add-sqr-sqrt_binary64`
105×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	246	28
2	2574	28

Stop Event

1×	node limit

Counts

4 → 77

Calls

4 calls:

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

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

728×	`sqr-pow_binary64`
438×	`associate-l_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
1	15	21
2	32	21
3	57	21
4	116	21
5	315	21
6	1143	21
7	1828	21
8	1915	21
9	2048	21
10	2206	21
11	2436	21
12	2758	21
13	3179	21
14	3679	21
15	4274	21
16	4996	21

Stop Event

1×	node limit

Counts

80 → 78

prune91.0ms (0.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	100	11	111

Error

0.1b

Counts

111 → 11

Alt Table

Status	Error	Program
	30.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (/.f64 (-.f64 (.f64 1/2025 (pow.f64 x 6)) (.f64 (.f64 x x) 1/9)) (fma.f64 1/45 (pow.f64 x 3) (*.f64 -1/3 x))))
	1.9b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (.f64 (cbrt.f64 x) 1/3)) 3) (*.f64 1/45 (pow.f64 x 3))))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (cbrt.f64 (.f64 1/3 x)) (pow.f64 (cbrt.f64 (.f64 1/3 x)) 2) (.f64 1/45 (pow.f64 x 3))))
	16.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (sqrt.f64 (.f64 x (cbrt.f64 x))) (.f64 (cbrt.f64 x) 1/3) (.f64 1/45 (pow.f64 x 3))))
✓	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/3) (*.f64 1/45 (pow.f64 x 3))))
	30.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (.f64 (-.f64 (.f64 1/2025 (pow.f64 x 6)) (.f64 (.f64 x x) 1/9)) (/.f64 1 (fma.f64 1/45 (pow.f64 x 3) (.f64 -1/3 x)))))
	16.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (.f64 (cbrt.f64 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)) (.f64 (cbrt.f64 x) 1/3) (*.f64 1/45 (pow.f64 x 3))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3))))
	33.7b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (pow.f64 (sqrt.f64 (fma.f64 1/3 x (.f64 1/45 (pow.f64 x 3)))) 2))
	33.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/3) (*.f64 1/45 (pow.f64 x 3))))
	2.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x))) 1/3) (.f64 1/45 (pow.f64 x 3))))

Compiler

Compiled 2549 to 1869 computations (26.7% saved)

regimes163.0ms (1.6%)

Accuracy

Total 0.2b remaining (69.6%)

Threshold costs 0.2b (69.6%)

Counts

78 → 1

Compiler

Compiled 3062 to 2440 computations (20.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	19	22

Stop Event

1×

saturated

end201.0ms (2%)

Compiler: Compiled 286 to 221 computations (22.7% saved)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	169	12
9	205	12
10	231	12
11	233	12

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	169	12
9	205	12
10	231	12
11	233	12

Details

analyze5.0ms (0.1%)

sample8.9s (87.4%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize4.0ms (0%)

series26.0ms (0.3%)

rewrite49.0ms (0.5%)

simplify35.0ms (0.3%)

prune72.0ms (0.7%)

localize8.0ms (0.1%)

series10.0ms (0.1%)

rewrite54.0ms (0.5%)

simplify60.0ms (0.6%)

prune124.0ms (1.2%)

localize8.0ms (0.1%)

series3.0ms (0%)

rewrite35.0ms (0.3%)

simplify63.0ms (0.6%)

prune76.0ms (0.7%)

localize11.0ms (0.1%)

series65.0ms (0.6%)

rewrite46.0ms (0.5%)

simplify62.0ms (0.6%)

prune91.0ms (0.9%)

regimes163.0ms (1.6%)

simplify2.0ms (0%)

end201.0ms (2%)

Profiling

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	169	12
9	205	12
10	231	12
11	233	12