Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.1s (59.7%)

Results

881.0ms	2049×	body	1024	valid
525.0ms	4397×	body	128	valid
338.0ms	1035×	body	512	valid
159.0ms	264×	body	2048	valid
112.0ms	511×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

26.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.6b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 N)
✓	3.1b	(-.f64 (log1p.f64 N) (log.f64 N))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (log1p.f64 N) (log.f64 N))
2.0ms	(log1p.f64 N)

rewrite48.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

541×	`expm1-log1p-u_binary64`
540×	`log1p-expm1-u_binary64`
394×	`prod-diff_binary64`
252×	`log-prod_binary64`
168×	`fma-def_binary64`

Counts

2 → 108

Calls

2 calls:

45.0ms	(log1p.f64 N)
45.0ms	(-.f64 (log1p.f64 N) (log.f64 N))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	105	11
2	1343	11
3	5012	11
0	0	0
1	0	0

simplify52.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-def_binary64`
379×	`times-frac_binary64`
324×	`fma-neg_binary64`
281×	`associate-+l+_binary64`
274×	`associate--l+_binary64`

Counts

132 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	376
1	163	350
2	443	346
3	1237	335
4	4414	335
5	5036	335

prune145.0ms (4.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	2	142

Error

0.0b

Counts

142 → 2

Alt Table

Status	Error	Program
▶	26.4b	(log.f64 (/.f64 (+.f64 N 1) N))
	35.0b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))

Compiler

Compiled 1994 to 843 computations (57.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.9b	(log.f64 (/.f64 (+.f64 N 1) N))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(log.f64 (/.f64 (+.f64 N 1) N))

rewrite152.0ms (4.3%)

Algorithm

2×	batch-egg-rewrite

Rules

635×	`log1p-expm1-u_binary64`
635×	`expm1-log1p-u_binary64`
292×	`log-prod_binary64`
115×	`fma-def_binary64`
108×	`log1p-udef_binary64`

Counts

1 → 66

Calls

1 calls:

150.0ms

(log.f64 (/.f64 (+.f64 N 1) N))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	126	8
2	1594	8
3	5240	8
0	0	0
1	0	0

simplify66.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
510×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`
285×	`associate-/l/_binary64`
261×	`div-sub_binary64`

Counts

78 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	186
1	93	184
2	225	184
3	589	181
4	1670	181
5	4250	181
6	4702	181
7	4908	181

prune31.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	80	2	82

Error

0.0b

Counts

82 → 2

Alt Table

Status	Error	Program
✓	26.4b	(log.f64 (/.f64 (+.f64 N 1) N))
▶	35.0b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))

Compiler

Compiled 1076 to 555 computations (48.4% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/3 (pow.f64 N 3))
✓	0.3b	(/.f64 1/4 (pow.f64 N 4))
✓	0.4b	(/.f64 1/2 (*.f64 N N))
✓	26.3b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))

series13.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

5.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
3.0ms	(/.f64 1/3 (pow.f64 N 3))
3.0ms	(/.f64 1/4 (pow.f64 N 4))
2.0ms	(/.f64 1/2 (*.f64 N N))

rewrite83.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

271×	`prod-diff_binary64`
204×	`log1p-expm1-u_binary64`
204×	`expm1-log1p-u_binary64`
196×	`add-sqr-sqrt_binary64`
192×	`add-cbrt-cube_binary64`

Counts

4 → 113

Calls

4 calls:

80.0ms	(/.f64 1/3 (pow.f64 N 3))
80.0ms	(/.f64 1/4 (pow.f64 N 4))
80.0ms	(/.f64 1/2 (*.f64 N N))
80.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	433	48
2	4738	48
3	5032	48
0	0	0
1	0	0

simplify50.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

847×	`distribute-neg-frac_binary64`
453×	`times-frac_binary64`
345×	`associate-l_binary64`
337×	`fma-def_binary64`
319×	`associate-/l/_binary64`

Counts

137 → 126

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	303
1	78	303
2	160	303
3	390	303
4	1055	303
5	3979	303
6	5015	303

prune142.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	124	4	128

Error

0.0b

Counts

128 → 4

Alt Table

Status	Error	Program
✓	26.4b	(log.f64 (/.f64 (+.f64 N 1) N))
▶	35.7b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4))))) 3)
	52.6b	(pow.f64 (pow.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4)))) 3) 1/3)
✓	35.0b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))

Compiler

Compiled 4176 to 3247 computations (22.2% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1/4 (pow.f64 N 4))
✓	0.4b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4))))) 3)
✓	18.1b	(cbrt.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4)))))
✓	26.3b	(-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4))))

series22.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

12.0ms

(pow.f64 (cbrt.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4))))) 3)

6.0ms

(cbrt.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4)))))

5.0ms

(-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4))))

rewrite91.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

698×	`prod-diff_binary64`
186×	`log1p-expm1-u_binary64`
186×	`expm1-log1p-u_binary64`
177×	`add-sqr-sqrt_binary64`
176×	`add-cbrt-cube_binary64`

Counts

3 → 144

Calls

3 calls:

86.0ms

(pow.f64 (cbrt.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4))))) 3)

86.0ms

(cbrt.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4)))))

86.0ms

(-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	83
1	418	83
2	4072	83
3	5132	83
0	0	0
1	0	0

simplify58.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

447×	`unswap-sqr_binary64`
365×	`associate-r_binary64`
344×	`fma-def_binary64`
306×	`associate-l_binary64`
290×	`sub-neg_binary64`

Counts

180 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	1106
1	344	1009
2	1040	847
3	3977	703
4	4971	703

prune152.0ms (4.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	154	4	158

Error

0.0b

Counts

158 → 4

Alt Table

Status	Error	Program
✓	26.4b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	35.7b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1/4 (pow.f64 N 4))))) 3)
✓	35.0b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
	37.9b	(pow.f64 (-.f64 (+.f64 (.f64 1/12 (pow.f64 (/.f64 1 (pow.f64 N 7)) 1/3)) (pow.f64 (/.f64 1 N) 1/3)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 N 4)) 1/3)) (*.f64 35/648 (pow.f64 (/.f64 1 (pow.f64 N 10)) 1/3)))) 3)

Compiler

Compiled 5436 to 4521 computations (16.8% saved)

regimes136.0ms (3.9%)

Accuracy

Total 0.0b remaining (5.5%)

Threshold costs 0.0b (5.5%)

Counts

49 → 2

Compiler

Compiled 1930 to 1530 computations (20.7% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	52
1	38	52
2	43	52
3	46	52
4	47	52
5	46	52

end108.0ms (3.1%)

Compiler: Compiled 162 to 131 computations (19.1% saved)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Details

analyze1.0ms (0%)

sample2.1s (59.7%)

simplify12.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite48.0ms (1.4%)

simplify52.0ms (1.5%)

prune145.0ms (4.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite152.0ms (4.3%)

simplify66.0ms (1.9%)

prune31.0ms (0.9%)

localize13.0ms (0.4%)

series13.0ms (0.4%)

rewrite83.0ms (2.4%)

simplify50.0ms (1.4%)

prune142.0ms (4.1%)

localize14.0ms (0.4%)

series22.0ms (0.6%)

rewrite91.0ms (2.6%)

simplify58.0ms (1.7%)

prune152.0ms (4.3%)

regimes136.0ms (3.9%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end108.0ms (3.1%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8