Details

analyze745.0ms (17.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
7%	92.8%	0.2%	8
19.1%	80.7%	0.2%	9
29.8%	70%	0.2%	10
31.3%	68.5%	0.2%	11
42.3%	57.2%	0.6%	12
53.3%	45.5%	1.2%	13
59.2%	39.3%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (24.9%)

Results

886.0ms	8256×	body	128	valid
68.0ms	594×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify115.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1630×	`fma-neg_binary64`
896×	`div-sub_binary64`
582×	`times-frac_binary64`
579×	`fma-def_binary64`
367×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	34	13
3	74	13
4	145	13
5	245	13
6	572	13
7	1407	13
8	2937	13
9	2993	13
10	3292	13
11	3338	13
12	3355	13
13	3404	13
14	4948	13

prune1.0ms (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

10.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.8b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	10.2b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

series37.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
6.0ms	(*.f64 x (-.f64 y z))

rewrite60.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
109×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Counts

2 → 66

Calls

2 calls:

59.0ms	(*.f64 x (-.f64 y z))
59.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	205	20
2	2981	20
3	5059	20
0	0	0
1	0	0

simplify96.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

531×	`times-frac_binary64`
451×	`fma-def_binary64`
439×	`associate-/l*_binary64`
366×	`associate--l+_binary64`
293×	`cancel-sign-sub-inv_binary64`

Counts

150 → 105

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	89	1753
1	280	1699
2	1049	1531
3	4796	1507
4	4970	1501
5	5019	1501

prune85.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97	8	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	8	106

Error

0.0b

Counts

106 → 8

Alt Table

Status	Error	Program
▶	2.1b	(*.f64 (/.f64 x 1) (/.f64 (-.f64 y z) (-.f64 t z)))
	10.5b	(.f64 (-.f64 y z) (.f64 x (/.f64 1 (-.f64 t z))))
	2.3b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	2.4b	(*.f64 x (/.f64 1 (/.f64 (-.f64 t z) (-.f64 y z))))
	10.8b	(/.f64 (+.f64 (.f64 y x) (.f64 (neg.f64 z) x)) (-.f64 t z))
	42.4b	(-.f64 (+.f64 (/.f64 (.f64 y x) t) (+.f64 (/.f64 (.f64 y (.f64 z x)) (pow.f64 t 2)) (/.f64 (.f64 y (.f64 (pow.f64 z 2) x)) (pow.f64 t 3)))) (+.f64 (/.f64 (.f64 z x) t) (/.f64 (*.f64 (pow.f64 z 2) x) (pow.f64 t 2))))
	10.4b	(*.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	31.1b	(neg.f64 (/.f64 (*.f64 z x) (-.f64 t z)))

Compiler

Compiled 2325 to 832 computations (64.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 t z))
✓	2.1b	(*.f64 (/.f64 x 1) (/.f64 (-.f64 y z) (-.f64 t z)))

series54.0ms (1.3%)

Counts

2 → 84

Calls

2 calls:

35.0ms	(*.f64 (/.f64 x 1) (/.f64 (-.f64 y z) (-.f64 t z)))
19.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

rewrite142.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
278×	`egg-rr`
119×	`add-sqr-sqrt_binary64`
113×	`log1p-expm1-u_binary64`
113×	`expm1-log1p-u_binary64`

Counts

2 → 278

Calls

2 calls:

129.0ms	(/.f64 (-.f64 y z) (-.f64 t z))
129.0ms	(*.f64 (/.f64 x 1) (/.f64 (-.f64 y z) (-.f64 t z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	233	23
2	3320	23
3	5187	23
0	0	0
1	0	0

simplify93.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
725×	`fma-neg_binary64`
656×	`times-frac_binary64`
500×	`cancel-sign-sub-inv_binary64`
337×	`sub-neg_binary64`

Counts

362 → 345

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	2603
1	468	2525
2	1780	2084
3	4462	2072
4	5008	2072

prune240.0ms (5.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	342	3	345
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	347	6	353

Error

Counts

353 → 6

Alt Table

Status	Error	Program
	10.8b	(/.f64 (+.f64 (.f64 y x) (.f64 (neg.f64 z) x)) (-.f64 t z))
▶	2.2b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	2.3b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	10.9b	(/.f64 (-.f64 y z) (*.f64 (/.f64 1 x) (-.f64 t z)))
	10.4b	(*.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	34.3b	(*.f64 (/.f64 x 1) (/.f64 y (-.f64 t z)))

Compiler

Compiled 15238 to 4325 computations (71.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 y z))
✓	2.1b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))

series52.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

32.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
19.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

rewrite140.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

979×	`prod-diff_binary64`
278×	`egg-rr`
115×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`
110×	`expm1-log1p-u_binary64`

Counts

2 → 278

Calls

2 calls:

126.0ms	(/.f64 (-.f64 t z) (-.f64 y z))
126.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	214	23
2	3301	23
3	5256	23
0	0	0
1	0	0

simplify102.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

830×	`times-frac_binary64`
731×	`fma-def_binary64`
663×	`fma-neg_binary64`
541×	`cancel-sign-sub-inv_binary64`
323×	`sub-neg_binary64`

Counts

362 → 344

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	2597
1	473	2531
2	1819	2289
3	4973	2289
4	5407	2289

prune221.0ms (5.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	343	1	344
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	345	5	350

Error

Counts

350 → 5

Alt Table

Status	Error	Program
▶	2.3b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	2.3b	(pow.f64 (/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) x) -1)
	10.9b	(/.f64 (-.f64 y z) (*.f64 (/.f64 1 x) (-.f64 t z)))
	10.8b	(/.f64 (+.f64 (.f64 y x) (.f64 (neg.f64 z) x)) (-.f64 t z))
	10.4b	(*.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

Compiler

Compiled 14859 to 3737 computations (74.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 t z))
✓	0.2b	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))
✓	2.1b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))

series62.0ms (1.4%)

Counts

3 → 108

Calls

3 calls:

33.0ms	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
20.0ms	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))
8.0ms	(/.f64 1 (-.f64 t z))

rewrite75.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

727×	`prod-diff_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
123×	`add-sqr-sqrt_binary64`
116×	`log1p-expm1-u_binary64`

Counts

3 → 84

Calls

3 calls:

74.0ms	(/.f64 1 (-.f64 t z))
74.0ms	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))
74.0ms	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	241	30
2	3157	30
3	5202	30
0	0	0
1	0	0

simplify98.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-def_binary64`
678×	`times-frac_binary64`
599×	`fma-neg_binary64`
500×	`cancel-sign-sub-inv_binary64`
345×	`sub-neg_binary64`

Counts

192 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	3095
1	526	3011
2	1961	2743
3	4952	2740
4	5324	2740

prune101.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	164	5	169

Error

Counts

169 → 5

Alt Table

Status	Error	Program
✓	2.3b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	2.3b	(pow.f64 (/.f64 (/.f64 (-.f64 t z) (-.f64 y z)) x) -1)
	10.9b	(/.f64 (-.f64 y z) (*.f64 (/.f64 1 x) (-.f64 t z)))
	10.8b	(/.f64 (+.f64 (.f64 y x) (.f64 (neg.f64 z) x)) (-.f64 t z))
	10.4b	(*.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

Compiler

Compiled 3537 to 1407 computations (60.2% saved)

regimes541.0ms (12.7%)

Accuracy

Total 2.0b remaining (99.3%)

Threshold costs 0b (0%)

Counts

91 → 3

Compiler

Compiled 6686 to 4378 computations (34.5% saved)

bsearch41.0ms (0.9%)

Steps

Iters	Range		Point
8	3.7444332502365777e-143	7.15706280371959e-139	6.0967477663018776e-139
8	-3.095848844879231e-209	-1.603738490821039e-212	-1.9332557615753545e-212

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`/-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54
1	28	54
2	33	54
3	35	54
4	36	54
5	35	54

end69.0ms (1.6%)

Compiler: Compiled 156 to 84 computations (46.2% saved)

Details

analyze745.0ms (17.5%)

sample1.1s (24.9%)

simplify115.0ms (2.7%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series37.0ms (0.9%)

rewrite60.0ms (1.4%)

simplify96.0ms (2.3%)

prune85.0ms (2%)

localize7.0ms (0.2%)

series54.0ms (1.3%)

rewrite142.0ms (3.3%)

simplify93.0ms (2.2%)

prune240.0ms (5.6%)

localize6.0ms (0.1%)

series52.0ms (1.2%)

rewrite140.0ms (3.3%)

simplify102.0ms (2.4%)

prune221.0ms (5.2%)

localize7.0ms (0.2%)

series62.0ms (1.4%)

rewrite75.0ms (1.8%)

simplify98.0ms (2.3%)

prune101.0ms (2.4%)

regimes541.0ms (12.7%)

bsearch41.0ms (0.9%)

simplify4.0ms (0.1%)

end69.0ms (1.6%)

Profiling