Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 21 to 17 computations (19% saved)

sample986.0ms (33.5%)

Results

873.0ms

8256×

body

128

valid

Compiler

Compiled 62 to 50 computations (19.4% saved)

simplify88.0ms (3%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
684×	`fma-neg_binary64`
640×	`associate-/l*_binary64`
583×	`associate-/r*_binary64`
496×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	34	22
2	59	22
3	94	22
4	131	22
5	171	20
6	250	20
7	423	20
8	810	20
9	1376	20
10	2197	20
11	2355	20
12	3878	20
13	4822	20
14	4656	20

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (.f64 x 4481/100000))))) x))
▶	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Status

Error

Program

0.1b

(*.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000))))) x))

▶

0.1b

(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 107 to 83 computations (22.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.2b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
✓	13.4b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series11.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(fma.f64 x 4481/100000 99229/100000)
3.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
2.0ms	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
1.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)

rewrite66.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

488×	`log-prod_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
176×	`log-pow_binary64`
157×	`prod-diff_binary64`

Counts

4 → 121

Calls

4 calls:

63.0ms	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
63.0ms	(fma.f64 x 4481/100000 99229/100000)
63.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
63.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	267	46
2	2886	46
3	5009	46
0	0	0
1	0	0

simplify88.0ms (3%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
417×	`times-frac_binary64`
342×	`sub-neg_binary64`
307×	`cancel-sign-sub-inv_binary64`
291×	`neg-mul-1_binary64`

Counts

169 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	500
1	166	448
2	388	436
3	956	420
4	2759	420
5	4400	420
6	4971	420
7	4923	420

prune173.0ms (5.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	153	5	158

Error

0.0b

Counts

158 → 5

Alt Table

Status	Error	Program
	0.1b	(.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (.f64 x 4481/100000))))) x))
	1.5b	(*.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2))
▶	0.1b	(pow.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) 1)
	14.3b	(/.f64 (-.f64 (.f64 (.f64 x -70711/100000) (.f64 x -70711/100000)) (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)) (-.f64 (.f64 x -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	0.1b	(fma.f64 x -70711/100000 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 3363 to 2609 computations (22.4% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	0.2b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
	13.4b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

prune233.0ms (7.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	156	5	161

Error

0.0b

Counts

161 → 5

Alt Table

Status	Error	Program
▶	0.1b	(.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (.f64 x 4481/100000))))) x))
	1.5b	(*.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2))
✓	0.1b	(pow.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) 1)
	14.3b	(/.f64 (-.f64 (.f64 (.f64 x -70711/100000) (.f64 x -70711/100000)) (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)) (-.f64 (.f64 x -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	0.1b	(fma.f64 x -70711/100000 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 3657 to 2907 computations (20.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (+.f64 99229/100000 (.f64 x 4481/100000)))
✓	0.3b	(*.f64 x 4481/100000)
✓	0.4b	(*.f64 x 27061/100000)
✓	13.4b	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))

series8.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))
2.0ms	(.f64 x (+.f64 99229/100000 (.f64 x 4481/100000)))
1.0ms	(*.f64 x 4481/100000)
1.0ms	(*.f64 x 27061/100000)

rewrite77.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

848×	`prod-diff_binary64`
155×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`
147×	`add-log-exp_binary64`

Counts

4 → 89

Calls

4 calls:

75.0ms	(.f64 x (+.f64 99229/100000 (.f64 x 4481/100000)))
75.0ms	(*.f64 x 4481/100000)
75.0ms	(*.f64 x 27061/100000)
75.0ms	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	318	32
2	4001	32
3	5532	32
0	0	0
1	0	0

simplify61.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
739×	`cancel-sign-sub-inv_binary64`
417×	`times-frac_binary64`
280×	`fma-def_binary64`
239×	`neg-mul-1_binary64`

Counts

137 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	400
1	120	396
2	275	383
3	689	357
4	2031	357
5	4619	357
6	5037	357

prune141.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	111	4	115

Error

0.0b

Counts

115 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 70711/100000 (-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x))
✓	0.1b	(pow.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) 1)
	14.3b	(/.f64 (-.f64 (.f64 (.f64 x -70711/100000) (.f64 x -70711/100000)) (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)) (-.f64 (.f64 x -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	1.5b	(*.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2))

Compiler

Compiled 2613 to 2062 computations (21.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 70711/100000 (-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x))
	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	13.4b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms

(fma.f64 x 27061/100000 230753/100000)

3.0ms

(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

2.0ms

(*.f64 70711/100000 (-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x))

rewrite67.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

600×	`prod-diff_binary64`
254×	`log1p-udef_binary64`
144×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`

Counts

3 → 77

Calls

3 calls:

61.0ms

(*.f64 70711/100000 (-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x))

61.0ms

(fma.f64 x 27061/100000 230753/100000)

61.0ms

(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	43
1	298	43
2	3450	43
3	4848	43
0	0	0
1	0	0

simplify67.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

559×	`fma-def_binary64`
541×	`times-frac_binary64`
360×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
272×	`fma-neg_binary64`

Counts

113 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	428
1	189	394
2	460	382
3	1147	366
4	3400	366
5	4737	366
6	4965	366

prune141.0ms (4.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	140	4	144

Error

0.0b

Counts

144 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 70711/100000 (-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x))
✓	0.1b	(pow.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) 1)
	14.3b	(/.f64 (-.f64 (.f64 (.f64 x -70711/100000) (.f64 x -70711/100000)) (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)) (-.f64 (.f64 x -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	1.5b	(*.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2))

Compiler

Compiled 2870 to 2242 computations (21.9% saved)

regimes563.0ms (19.1%)

Accuracy

Total 0.0b remaining (24.7%)

Threshold costs 0.0b (24.7%)

Counts

156 → 1

Compiler

Compiled 8312 to 6542 computations (21.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	23
1	18	23
2	17	23

end110.0ms (3.7%)

Compiler: Compiled 147 to 114 computations (22.4% saved)

Details

analyze5.0ms (0.2%)

sample986.0ms (33.5%)

simplify88.0ms (3%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series11.0ms (0.4%)

rewrite66.0ms (2.2%)

simplify88.0ms (3%)

prune173.0ms (5.9%)

localize13.0ms (0.5%)

prune233.0ms (7.9%)

localize12.0ms (0.4%)

series8.0ms (0.3%)

rewrite77.0ms (2.6%)

simplify61.0ms (2.1%)

prune141.0ms (4.8%)

localize9.0ms (0.3%)

series8.0ms (0.3%)

rewrite67.0ms (2.3%)

simplify67.0ms (2.3%)

prune141.0ms (4.8%)

regimes563.0ms (19.1%)

simplify2.0ms (0.1%)

end110.0ms (3.7%)

Profiling