Details

analyze6.0ms (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)

sample8.8s (85.6%)

Results

6.8s	4108×	body	2048	valid
1.3s	2110×	body	1024	valid
329.0ms	1056×	body	512	valid
193.0ms	228×	body	4096	valid
104.0ms	504×	body	256	valid
30.0ms	250×	body	128	valid

Compiler

Compiled 32 to 24 computations (25% saved)

preprocess21.0ms (0.2%)

Algorithm

2×	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
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 7 computations (22.2% 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

59.7b

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)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.0b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series10.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

4.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))	x	inf
4.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))	x	-inf
1.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))	x	0

rewrite60.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	161	12
2	2343	12

Stop Event

1×	node limit

Counts

1 → 102

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

624×	`unswap-sqr_binary64`
539×	`fma-def_binary64`
516×	`sqr-pow_binary64`
302×	`associate-l_binary64`
221×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	162
1	69	162
2	149	162
3	368	162
4	673	162
5	1415	162
6	2081	162
7	3072	162
8	3288	162
9	3615	162
10	4018	162
11	4550	162

Stop Event

1×	node limit

Counts

114 → 112

prune60.0ms (0.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

113 → 1

Alt Table

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

Compiler

Compiled 2570 to 1582 computations (38.4% saved)

localize22.0ms (0.2%)

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)

series11.0ms (0.1%)

Counts

4 → 9

Calls

12 calls:

1.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))	x	-inf
1.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))	x	inf
1.0ms	(*.f64 2/945 (pow.f64 x 5))	x	inf
1.0ms	(*.f64 2/945 (pow.f64 x 5))	x	-inf
1.0ms	(*.f64 2/945 (pow.f64 x 5))	x	0

rewrite56.0ms (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

simplify61.0ms (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

prune109.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	10	112

Error

0.1b

Counts

112 → 10

Alt Table

Status	Error	Program
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
	30.8b	(+.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))))
	30.8b	(+.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))
	40.9b	(+.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))) (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)))))
	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))))
	28.7b	(+.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)))))
▶	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 1/45 (pow.f64 x 3))))
	28.6b	(+.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))))
	1.6b	(+.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))))

Compiler

Compiled 2662 to 2142 computations (19.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series77.0ms (0.8%)

Counts

4 → 3

Calls

12 calls:

18.0ms	(pow.f64 (cbrt.f64 x) 2)	x	-inf
18.0ms	(fma.f64 (.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 1/45 (pow.f64 x 3)))	x	-inf
14.0ms	(*.f64 1/3 (pow.f64 (cbrt.f64 x) 2))	x	-inf
8.0ms	(cbrt.f64 x)	x	-inf
4.0ms	(fma.f64 (.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 1/45 (pow.f64 x 3)))	x	inf

rewrite55.0ms (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	39
1	246	31
2	2571	31

Stop Event

1×	node limit

Counts

4 → 77

simplify69.0ms (0.7%)

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

prune94.0ms (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	101	10	111

Error

0.1b

Counts

111 → 10

Alt Table

Status	Error	Program
▶	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
	1.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (pow.f64 (.f64 (cbrt.f64 x) (sqrt.f64 1/3)) 2) (cbrt.f64 x) (*.f64 1/45 (pow.f64 x 3))))
	30.8b	(+.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))))
	30.8b	(+.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))
	40.9b	(+.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))) (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)))))
	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))))
	28.7b	(+.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)))))
	28.6b	(+.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))))
	12.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (sqrt.f64 (.f64 (.f64 x (cbrt.f64 x)) 1/9)) (cbrt.f64 x) (.f64 1/45 (pow.f64 x 3))))

Compiler

Compiled 2737 to 2019 computations (26.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series51.0ms (0.5%)

Counts

2 → 0

Calls

6 calls:

19.0ms	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)	x	-inf
14.0ms	(cbrt.f64 (*.f64 1/3 x))	x	-inf
6.0ms	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)	x	0
6.0ms	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)	x	inf
3.0ms	(cbrt.f64 (*.f64 1/3 x))	x	0

rewrite37.0ms (0.4%)

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

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

104 → 104

prune126.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	133	13	146

Error

0.1b

Counts

146 → 13

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
	1.6b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (pow.f64 (.f64 (cbrt.f64 x) (sqrt.f64 1/3)) 2) (cbrt.f64 x) (*.f64 1/45 (pow.f64 x 3))))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2) (cbrt.f64 1/3)) (cbrt.f64 x))))
	40.9b	(+.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))) (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)))))
	30.8b	(+.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))))
	30.8b	(+.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))
	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))))
	28.7b	(+.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)))))
	28.6b	(+.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))))
	12.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (fma.f64 (sqrt.f64 (.f64 (.f64 x (cbrt.f64 x)) 1/9)) (cbrt.f64 x) (.f64 1/45 (pow.f64 x 3))))
	30.3b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 1/3 x)) 2)) 3/2) (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x))) 3/2))))
	1.5b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.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)))))
	1.8b	(+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 1/3 x)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 x))) (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2)))))

Compiler

Compiled 3532 to 2918 computations (17.4% saved)

regimes188.0ms (1.8%)

Accuracy

Total 0.2b remaining (71.5%)

Threshold costs 0.2b (71.5%)

Counts

87 → 1

Compiler

Compiled 3832 to 3172 computations (17.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	16	20

Stop Event

1×

saturated

end250.0ms (2.4%)

Stop Event

1×

fuel

Compiler

Compiled 360 to 290 computations (19.4% 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
0	1	1

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
0	1	1

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

analyze6.0ms (0.1%)

sample8.8s (85.6%)

preprocess21.0ms (0.2%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series10.0ms (0.1%)

rewrite60.0ms (0.6%)

simplify59.0ms (0.6%)

prune60.0ms (0.6%)

localize22.0ms (0.2%)

series11.0ms (0.1%)

rewrite56.0ms (0.5%)

simplify61.0ms (0.6%)

prune109.0ms (1.1%)

localize12.0ms (0.1%)

series77.0ms (0.8%)

rewrite55.0ms (0.5%)

simplify69.0ms (0.7%)

prune94.0ms (0.9%)

localize12.0ms (0.1%)

series51.0ms (0.5%)

rewrite37.0ms (0.4%)

simplify11.0ms (0.1%)

prune126.0ms (1.2%)

regimes188.0ms (1.8%)

simplify2.0ms (0%)

end250.0ms (2.4%)

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
0	1	1

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