Details

analyze160.0ms (2.1%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample1.8s (23.1%)

Results

1.6s	8256×	body	128	valid
31.0ms	222×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
148×	`fma-neg_binary64`
84×	`distribute-rgt-in_binary64`
50×	`distribute-lft-in_binary64`
50×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

prune3.0ms (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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

series15.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

rewrite71.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

692×	`log1p-expm1-u_binary64`
692×	`expm1-log1p-u_binary64`
132×	`prod-diff_binary64`
131×	`fma-def_binary64`
128×	`expm1-udef_binary64`

Counts

1 → 51

Calls

1 calls:

69.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	144	10
2	1759	10
3	4956	10
0	0	0
1	0	0

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

423×	`fma-neg_binary64`
367×	`neg-sub0_binary64`
365×	`distribute-rgt-neg-in_binary64`
361×	`neg-mul-1_binary64`
345×	`associate-r_binary64`

Counts

75 → 58

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	232
1	41	232
2	78	232
3	166	232
4	444	232
5	1310	232
6	2464	232
7	4517	232
8	4907	232

prune68.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	5	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	6	59

Error

0.0b

Counts

59 → 6

Alt Table

Status	Error	Program
▶	0.1b	(.f64 y (.f64 (-.f64 1 y) x))
	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	30.2b	(pow.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 2)
	1.2b	(pow.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 3)
	13.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 y 3)) (.f64 x y)) (+.f64 1 (fma.f64 y y y)))

Compiler

Compiled 810 to 303 computations (62.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 y) x)
✓	0.1b	(.f64 y (.f64 (-.f64 1 y) x))

series19.0ms (0.2%)

Counts

2 → 28

Calls

2 calls:

13.0ms	(.f64 y (.f64 (-.f64 1 y) x))
6.0ms	(*.f64 (-.f64 1 y) x)

rewrite103.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

693×	`log1p-expm1-u_binary64`
693×	`expm1-log1p-u_binary64`
132×	`prod-diff_binary64`
128×	`expm1-udef_binary64`
127×	`log1p-udef_binary64`

Counts

2 → 46

Calls

2 calls:

102.0ms	(*.f64 (-.f64 1 y) x)
102.0ms	(.f64 y (.f64 (-.f64 1 y) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	144	17
2	1761	17
3	4990	17
4	5002	17
0	0	0
1	0	0

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

487×	`unsub-neg_binary64`
379×	`fma-neg_binary64`
378×	`distribute-rgt-in_binary64`
315×	`associate-l_binary64`
301×	`distribute-lft-in_binary64`

Counts

74 → 56

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	228
1	40	228
2	71	228
3	150	228
4	392	228
5	1317	228
6	2563	228
7	4317	228
8	4909	228
9	4984	228
10	4827	228

prune67.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	56	6	62

Error

0.0b

Counts

62 → 6

Alt Table

Status	Error	Program
	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	30.0b	(.f64 y (cbrt.f64 (pow.f64 (.f64 (-.f64 1 y) x) 3)))
	30.2b	(pow.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 2)
▶	1.2b	(pow.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 3)
	13.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 y 3)) (.f64 x y)) (+.f64 1 (fma.f64 y y y)))

Compiler

Compiled 689 to 406 computations (41.1% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 3)
✓	8.7b	(cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))

series2.0s (25.9%)

Counts

2 → 48

Calls

2 calls:

1.3s	(pow.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 3)
666.0ms	(cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))

rewrite77.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

856×	`log1p-expm1-u_binary64`
856×	`expm1-log1p-u_binary64`
132×	`prod-diff_binary64`
90×	`add-sqr-sqrt_binary64`
85×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

75.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 3)
75.0ms	(cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	192	22
2	2197	22
3	5413	22
0	0	0
1	0	0

simplify151.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

814×	`fma-neg_binary64`
263×	`fma-def_binary64`
233×	`sub-neg_binary64`
221×	`associate-r_binary64`
176×	`associate-l_binary64`

Counts

121 → 117

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	111	1791
1	314	1631
2	914	1326
3	3417	903
4	4766	852
5	4980	852
6	4941	852

prune206.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	171	4	175
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	174	7	181

Error

0.0b

Counts

181 → 7

Alt Table

Status	Error	Program
	5.3b	(.f64 x (.f64 y (-.f64 1 y)))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
▶	1.2b	(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) (-.f64 1 y)))
	30.0b	(.f64 y (cbrt.f64 (pow.f64 (.f64 (-.f64 1 y) x) 3)))
	30.2b	(pow.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 2)
	13.1b	(.f64 (sqrt.f64 (-.f64 1 y)) (.f64 (sqrt.f64 (-.f64 1 y)) (*.f64 x y)))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 y (-.f64 1 y))))

Compiler

Compiled 3159 to 1821 computations (42.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 (.f64 x y)) (-.f64 1 y))
✓	0.3b	(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) (-.f64 1 y)))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
✓	8.7b	(cbrt.f64 (*.f64 x y))

series1.7s (22.5%)

Counts

4 → 96

Calls

4 calls:

643.0ms	(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
630.0ms	(cbrt.f64 (*.f64 x y))
418.0ms	(.f64 (cbrt.f64 (.f64 x y)) (-.f64 1 y))
54.0ms	(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) (-.f64 1 y)))

rewrite98.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

514×	`log-prod_binary64`
261×	`pow2_binary64`
188×	`pow1/3_binary64`
180×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`

Counts

4 → 159

Calls

4 calls:

93.0ms	(.f64 (cbrt.f64 (.f64 x y)) (-.f64 1 y))
93.0ms	(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) (-.f64 1 y)))
93.0ms	(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
93.0ms	(cbrt.f64 (*.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	224	35
2	2475	35
3	4963	35
0	0	0
1	0	0

simplify132.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

530×	`times-frac_binary64`
438×	`fma-neg_binary64`
365×	`cancel-sign-sub-inv_binary64`
303×	`fma-def_binary64`
302×	`difference-of-squares_binary64`

Counts

255 → 194

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	66	1594
1	183	1592
2	341	1408
3	1036	1040
4	2657	1016
5	4025	1016
6	5283	1016

prune238.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	227	8	235

Error

0.0b

Counts

235 → 8

Alt Table

Status	Error	Program
	5.3b	(.f64 x (.f64 y (-.f64 1 y)))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
✓	1.2b	(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) (-.f64 1 y)))
	1.5b	(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x y))) 3) (-.f64 1 y)))
	1.1b	(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 1 y)))
	30.2b	(pow.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 2)
	13.1b	(.f64 (sqrt.f64 (-.f64 1 y)) (.f64 (sqrt.f64 (-.f64 1 y)) (*.f64 x y)))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 y (-.f64 1 y))))

Compiler

Compiled 4192 to 1862 computations (55.6% saved)

regimes315.0ms (4.1%)

Accuracy

Total 0.1b remaining (76.3%)

Threshold costs 0.1b (76.3%)

Counts

62 → 1

Compiler

Compiled 2406 to 1574 computations (34.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	15	13
2	22	13
3	33	13
4	38	13
5	41	13
6	42	13
7	42	13

end174.0ms (2.2%)

Compiler: Compiled 135 to 88 computations (34.8% saved)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Details

analyze160.0ms (2.1%)

sample1.8s (23.1%)

simplify38.0ms (0.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series15.0ms (0.2%)

rewrite71.0ms (0.9%)

simplify93.0ms (1.2%)

prune68.0ms (0.9%)

localize8.0ms (0.1%)

series19.0ms (0.2%)

rewrite103.0ms (1.3%)

simplify137.0ms (1.8%)

prune67.0ms (0.9%)

localize12.0ms (0.2%)

series2.0s (25.9%)

rewrite77.0ms (1%)

simplify151.0ms (1.9%)

prune206.0ms (2.6%)

localize16.0ms (0.2%)

series1.7s (22.5%)

rewrite98.0ms (1.3%)

simplify132.0ms (1.7%)

prune238.0ms (3.1%)

regimes315.0ms (4.1%)

simplify4.0ms (0%)

end174.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10