Details

analyze578.0ms (13%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
45.2%	53.8%	0.9%	9
50.3%	47.8%	1.9%	10
54%	43.6%	2.4%	11
61.7%	32.9%	5.4%	12
64.1%	28.3%	7.6%	13
66.2%	24.7%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (30.5%)

Results

1.0s	8256×	body	128	valid
185.0ms	1205×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1167×	`fma-def_binary64`
1073×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	43	18
3	75	18
4	123	16
5	213	16
6	302	16
7	472	16
8	1009	13
9	1328	13
10	1542	13
11	1559	13
12	1556	13
13	1556	13
14	1453	13

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
	3.1b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	2.4b	(*.f64 (/.f64 x y) z)

series39.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

20.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
13.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

3 → 117

Calls

3 calls:

10.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
5.0ms	(*.f64 (/.f64 x y) z)
4.0ms	(/.f64 (+.f64 x 4) y)

simplify127.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-l_binary64`
381×	`fma-def_binary64`
379×	`associate-*l/_binary64`
369×	`associate-r_binary64`
310×	`fma-neg_binary64`

Counts

213 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	187	3147
1	457	2896
2	1229	2394
3	3977	2382
4	4927	2330
5	4911	2330

prune156.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	172	7	179

Error

Counts

179 → 7

Alt Table

Status	Error	Program
	30.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
	31.2b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	3.1b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
	32.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))
✓	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 3721 to 1769 computations (52.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)
✓	1.2b	(*.f64 (/.f64 x (cbrt.f64 y)) z)
✓	2.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))

series583.0ms (13.1%)

Counts

4 → 96

Calls

4 calls:

464.0ms	(*.f64 (/.f64 x (cbrt.f64 y)) z)
46.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))
39.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
33.0ms	(cbrt.f64 y)

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
45×	`add-sqr-sqrt_binary64`
35×	`associate-l_binary64`
35×	`add-cbrt-cube_binary64`

Counts

4 → 152

Calls

4 calls:

12.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))
6.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
6.0ms	(*.f64 (/.f64 x (cbrt.f64 y)) z)
1.0ms	(cbrt.f64 y)

simplify127.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-neg_binary64`
610×	`associate-/l/_binary64`
454×	`*-commutative_binary64`
384×	`unswap-sqr_binary64`
192×	`associate-r_binary64`

Counts

248 → 224

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3394
1	393	2332
2	1491	2271
3	2499	2256
4	4837	2256
5	5214	2256

prune209.0ms (4.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	260	7	267

Error

Counts

267 → 7

Alt Table

Status	Error	Program
	30.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
	31.2b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
▶	3.1b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
✓	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
	32.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))
✓	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 7168 to 3014 computations (58% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (fma.f64 x z -4))
✓	2.9b	(/.f64 (-.f64 x (fma.f64 x z -4)) y)

series19.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(/.f64 (-.f64 x (fma.f64 x z -4)) y)
4.0ms	(-.f64 x (fma.f64 x z -4))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
9×	`prod-diff_binary64`

Counts

2 → 71

Calls

2 calls:

5.0ms	(/.f64 (-.f64 x (fma.f64 x z -4)) y)
3.0ms	(-.f64 x (fma.f64 x z -4))

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-neg_binary64`
446×	`associate-l_binary64`
420×	`div-sub_binary64`
358×	`associate-r_binary64`
297×	`fma-def_binary64`

Counts

131 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2146
1	314	2027
2	864	1648
3	3571	1648
4	4943	1648

prune192.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	126	6	132

Error

Counts

132 → 6

Alt Table

Status	Error	Program
	3.1b	(fabs.f64 (-.f64 (/.f64 x y) (/.f64 (fma.f64 x z -4) y)))
▶	3.1b	(fabs.f64 (/.f64 (fma.f64 x (-.f64 1 z) 4) y))
✓	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
	32.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))
✓	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	30.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))

Compiler

Compiled 2438 to 1483 computations (39.2% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1 z) 4)
✓	2.9b	(/.f64 (fma.f64 x (-.f64 1 z) 4) y)

series20.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

16.0ms	(/.f64 (fma.f64 x (-.f64 1 z) 4) y)
4.0ms	(fma.f64 x (-.f64 1 z) 4)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 x (-.f64 1 z) 4) y)
0.0ms	(fma.f64 x (-.f64 1 z) 4)

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

488×	`unsub-neg_binary64`
437×	`fma-neg_binary64`
317×	`times-frac_binary64`
313×	`distribute-rgt-in_binary64`
302×	`distribute-lft-in_binary64`

Counts

99 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1544
1	172	1481
2	394	1286
3	824	1193
4	3792	1193
5	5192	1193

prune46.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	66	6	72

Error

Counts

72 → 6

Alt Table

Status	Error	Program
	3.1b	(fabs.f64 (-.f64 (/.f64 x y) (/.f64 (fma.f64 x z -4) y)))
✓	3.1b	(fabs.f64 (/.f64 (fma.f64 x (-.f64 1 z) 4) y))
✓	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
	32.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))
✓	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	30.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))

Compiler

Compiled 1044 to 691 computations (33.8% saved)

regimes538.0ms (12.1%)

Accuracy

Total 0.1b remaining (81%)

Threshold costs 0.1b (81%)

Counts

70 → 3

Compiler

Compiled 5817 to 3881 computations (33.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
12×	`sub-neg_binary64`
9×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	94
1	36	94
2	56	94
3	74	94
4	90	94
5	97	94
6	98	94
7	97	94

end97.0ms (2.2%)

Compiler: Compiled 239 to 137 computations (42.7% saved)

Details

analyze578.0ms (13%)

sample1.4s (30.5%)

simplify64.0ms (1.4%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series39.0ms (0.9%)

rewrite26.0ms (0.6%)

simplify127.0ms (2.9%)

prune156.0ms (3.5%)

localize14.0ms (0.3%)

series583.0ms (13.1%)

rewrite37.0ms (0.8%)

simplify127.0ms (2.9%)

prune209.0ms (4.7%)

localize6.0ms (0.1%)

series19.0ms (0.4%)

rewrite13.0ms (0.3%)

simplify80.0ms (1.8%)

prune192.0ms (4.3%)

localize9.0ms (0.2%)

series20.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify80.0ms (1.8%)

prune46.0ms (1%)

regimes538.0ms (12.1%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end97.0ms (2.2%)

Profiling