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)

sample9.0s (84.8%)

Results

7.0s	4207×	body	2048	valid
1.2s	1970×	body	1024	valid
346.0ms	1050×	body	512	valid
192.0ms	219×	body	4096	valid
174.0ms	545×	body	256	valid
37.0ms	265×	body	128	valid

Compiler

Compiled 41 to 31 computations (24.4% saved)

simplify11.0ms (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

59.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.7b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 35 to 26 computations (25.7% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (tan.f64 x))
✓	5.0b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series27.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

17.0ms	(/.f64 1 (tan.f64 x))
10.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite55.0ms (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:

52.0ms	(/.f64 1 (tan.f64 x))
52.0ms	(-.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

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	2	145

Error

0.3b

Counts

145 → 2

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))))
	0.5b	(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))

Compiler

Compiled 2979 to 1857 computations (37.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/4725 (pow.f64 x 7))
✓	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.1b	(*.f64 2/945 (pow.f64 x 5))
✓	0.3b	(*.f64 1/3 x)

series11.0ms (0.1%)

Counts

4 → 0

Calls

4 calls:

3.0ms	(*.f64 1/4725 (pow.f64 x 7))
3.0ms	(*.f64 2/945 (pow.f64 x 5))
3.0ms	(*.f64 1/45 (pow.f64 x 3))
1.0ms	(*.f64 1/3 x)

rewrite51.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

622×	`log-prod_binary64`
266×	`expm1-udef_binary64`
266×	`log1p-udef_binary64`
224×	`log-pow_binary64`
157×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	340	25
2	3577	25

Stop Event

1×	node limit

Counts

4 → 64

Calls

4 calls:

50.0ms	(*.f64 1/4725 (pow.f64 x 7))
50.0ms	(*.f64 1/45 (pow.f64 x 3))
50.0ms	(*.f64 2/945 (pow.f64 x 5))
50.0ms	(*.f64 1/3 x)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

64 → 64

prune87.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	60	6	66

Error

0.2b

Counts

66 → 6

Alt Table

Status	Error	Program
▶	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (log.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3))) (*.f64 1/3 x))))
	38.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (pow.f64 (.f64 1/3 x) 3)))))
	46.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (sqrt.f64 (.f64 (*.f64 x x) 1/9)))))
	35.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (pow.f64 (sqrt.f64 (.f64 1/3 x)) 2))))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (pow.f64 (cbrt.f64 (.f64 1/3 x)) 3))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))))

Compiler

Compiled 1889 to 1569 computations (16.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 1/4725 (pow.f64 x 7))
	0.1b	(*.f64 2/945 (pow.f64 x 5))
	0.3b	(*.f64 1/3 x)
✓	2.4b	(log.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3)))

series270.0ms (2.6%)

Counts

1 → 12

Calls

1 calls:

270.0ms

(log.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3)))

rewrite31.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

630×	`log1p-expm1-u_binary64`
630×	`expm1-log1p-u_binary64`
309×	`log-prod_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	166	7
2	1796	7

Stop Event

1×	node limit

Counts

1 → 41

Calls

1 calls:

30.0ms

(log.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3)))

simplify67.0ms (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	84
1	15	84
2	32	84
3	57	84
4	116	84
5	315	84
6	1143	84
7	1828	84
8	1915	84
9	2048	84
10	2206	84
11	2436	84
12	2758	84
13	3179	84
14	3679	84
15	4274	84
16	4996	84

Stop Event

1×	node limit

Counts

53 → 41

prune107.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	89	6	95

Error

0.2b

Counts

95 → 6

Alt Table

Status	Error	Program
✓	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (log.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3))) (*.f64 1/3 x))))
	38.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (pow.f64 (.f64 1/3 x) 3)))))
	46.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (sqrt.f64 (.f64 (*.f64 x x) 1/9)))))
	35.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (pow.f64 (sqrt.f64 (.f64 1/3 x)) 2))))
▶	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (pow.f64 (cbrt.f64 (.f64 1/3 x)) 3))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))))

Compiler

Compiled 2590 to 2148 computations (17.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 2/945 (pow.f64 x 5))
	0.3b	(*.f64 1/3 x)
✓	0.6b	(cbrt.f64 (*.f64 1/3 x))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)

series98.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

59.0ms	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
38.0ms	(cbrt.f64 (*.f64 1/3 x))

rewrite36.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

487×	`log1p-expm1-u_binary64`
487×	`expm1-log1p-u_binary64`
439×	`unpow-prod-down_binary64`
247×	`log-prod_binary64`
139×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	141	10
2	1377	10

Stop Event

1×	node limit

Counts

2 → 104

Calls

2 calls:

35.0ms	(cbrt.f64 (*.f64 1/3 x))
35.0ms	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

828×	`sqr-pow_binary64`
416×	`unswap-sqr_binary64`
388×	`pow-sqr_binary64`
332×	`cube-prod_binary64`
240×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	152
1	27	152
2	44	152
3	81	152
4	198	152
5	609	152
6	904	152
7	1549	152
8	1662	152
9	1827	152
10	2045	152
11	2378	152
12	2837	152
13	3437	152
14	4193	152

Stop Event

1×	node limit

Counts

128 → 107

prune138.0ms (1.3%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	130	9	139
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	130	15	145

Error

0.1b

Counts

145 → 15

Alt Table

Status	Error	Program
	1.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (cbrt.f64 1/3) (.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (.f64 1/3 x)) 2))))))
✓	0.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (log.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3))) (*.f64 1/3 x))))
	1.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/3)))))
	38.2b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (pow.f64 (.f64 1/3 x) 3)))))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (cbrt.f64 (.f64 1/3 x)) (pow.f64 (cbrt.f64 (.f64 1/3 x)) 2)))))
	46.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (sqrt.f64 (.f64 (*.f64 x x) 1/9)))))
	1.9b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (pow.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 x)) 3))))
	35.1b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (pow.f64 (sqrt.f64 (.f64 1/3 x)) 2))))
	35.0b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/3)))))
✓	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (pow.f64 (cbrt.f64 (.f64 1/3 x)) 3))))
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))))
	2.7b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 x))) 3) 3))))
	2.4b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 1/3 x)) 2))) 3))))
	35.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 1/3 x)) 2))) 3/2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 x))) 3/2)))))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/4725 (pow.f64 x 7)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))))

Compiler

Compiled 4518 to 3748 computations (17% saved)

regimes55.0ms (0.5%)

Accuracy

Total 0.2b remaining (59.2%)

Threshold costs 0.2b (59.2%)

Counts

24 → 1

Compiler

Compiled 1164 to 956 computations (17.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	26	31

Stop Event

1×

saturated

end329.0ms (3.1%)

Compiler: Compiled 462 to 382 computations (17.3% 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%)

sample9.0s (84.8%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0%)

series27.0ms (0.3%)

rewrite55.0ms (0.5%)

simplify35.0ms (0.3%)

prune72.0ms (0.7%)

localize13.0ms (0.1%)

series11.0ms (0.1%)

rewrite51.0ms (0.5%)

simplify6.0ms (0.1%)

prune87.0ms (0.8%)

localize14.0ms (0.1%)

series270.0ms (2.6%)

rewrite31.0ms (0.3%)

simplify67.0ms (0.6%)

prune107.0ms (1%)

localize16.0ms (0.2%)

series98.0ms (0.9%)

rewrite36.0ms (0.3%)

simplify62.0ms (0.6%)

prune138.0ms (1.3%)

regimes55.0ms (0.5%)

simplify2.0ms (0%)

end329.0ms (3.1%)

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