Details

analyze78.0ms (1.8%)

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%	50%	12.6%	6
50%	37.5%	12.6%	7
56.2%	25%	18.8%	8
62.4%	18.7%	18.8%	9
65.6%	12.5%	22%	10
68.7%	9.4%	22%	11
70.2%	6.2%	23.5%	12
71.8%	4.7%	23.5%	13
72.6%	3.1%	24.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample719.0ms (16.8%)

Results

665.0ms	8256×	body	128	valid
8.0ms	97×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

265×	`fma-def_binary64`
84×	`fma-neg_binary64`
35×	`distribute-rgt-in_binary64`
26×	`unsub-neg_binary64`
25×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

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

0.1b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series10.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

6.0ms	(.f64 x (-.f64 1 (.f64 x y)))
3.0ms	(-.f64 1 (*.f64 x y))

rewrite46.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

682×	`log1p-expm1-u_binary64`
682×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
73×	`add-sqr-sqrt_binary64`
67×	`add-cbrt-cube_binary64`

Counts

2 → 51

Calls

2 calls:

45.0ms	(-.f64 1 (*.f64 x y))
45.0ms	(.f64 x (-.f64 1 (.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	145	17
2	1739	17
3	4964	17
0	0	0
1	0	0

simplify191.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1481×	`fma-def_binary64`
1010×	`distribute-rgt-in_binary64`
714×	`fma-neg_binary64`
510×	`distribute-rgt-neg-in_binary64`
467×	`cancel-sign-sub-inv_binary64`

Counts

99 → 61

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	13	370
1	35	370
2	60	370
3	120	370
4	292	370
5	909	370
6	1453	370
7	2397	370
8	3261	370
9	3801	282
10	3069	282
11	4317	282
12	4436	282
13	4715	282
14	4864	282
15	4895	282
16	4820	282

prune47.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	55	6	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	7	62

Error

0.0b

Counts

62 → 7

Alt Table

Status	Error	Program
	8.2b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
	6.1b	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (*.f64 x y))))
	10.6b	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 3)) (+.f64 1 (+.f64 (.f64 x y) (pow.f64 (.f64 x y) 2)))))
	6.1b	(.f64 x (/.f64 1 (/.f64 (+.f64 1 (.f64 x y)) (-.f64 1 (pow.f64 (*.f64 x y) 2)))))
▶	1.4b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	8.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) x) (+.f64 1 (*.f64 x y)))

Compiler

Compiled 912 to 516 computations (43.4% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 1 (*.f64 x y))
	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	0.6b	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)

series1.3s (31.4%)

Counts

2 → 48

Calls

2 calls:

1.3s	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
29.0ms	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))

rewrite63.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
86×	`add-cbrt-cube_binary64`

Counts

2 → 65

Calls

2 calls:

61.0ms	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))
61.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	193	22
2	2175	22
3	5885	22
0	0	0
1	0	0

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

916×	`times-frac_binary64`
370×	`fma-def_binary64`
309×	`fma-neg_binary64`
299×	`cancel-sign-sub-inv_binary64`
154×	`distribute-neg-frac_binary64`

Counts

113 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	2130
1	439	2060
2	1520	1912
3	4691	1836
4	4954	1836

prune139.0ms (3.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	183	9	192

Error

Counts

192 → 9

Alt Table

Status	Error	Program
	8.2b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
	6.1b	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (*.f64 x y))))
	29.3b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	10.6b	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 3)) (+.f64 1 (+.f64 (.f64 x y) (pow.f64 (.f64 x y) 2)))))
▶	0.5b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x))
	6.1b	(.f64 x (/.f64 1 (/.f64 (+.f64 1 (.f64 x y)) (-.f64 1 (pow.f64 (*.f64 x y) 2)))))
✓	1.4b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	8.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) x) (+.f64 1 (*.f64 x y)))

Compiler

Compiled 4131 to 2762 computations (33.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x))
✓	0.1b	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x)
✓	0.2b	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x y))) 2)
✓	0.2b	(cbrt.f64 (-.f64 1 (*.f64 x y)))

series83.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

37.0ms	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x y))) 2)
21.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x)
16.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))
8.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x))

rewrite95.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

521×	`log-prod_binary64`
433×	`prod-diff_binary64`
182×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
161×	`log-pow_binary64`

Counts

4 → 88

Calls

4 calls:

94.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x))
94.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x)
94.0ms	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x y))) 2)
94.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	226	41
2	2482	41
3	4979	41
4	4937	41
0	0	0
1	0	0

simplify123.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

728×	`fma-neg_binary64`
632×	`cancel-sign-sub-inv_binary64`
280×	`distribute-neg-frac_binary64`
276×	`distribute-rgt-neg-in_binary64`
268×	`sub-neg_binary64`

Counts

184 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	3680
1	752	3552
2	2575	3350
3	4910	3342
4	5368	3342

prune257.0ms (6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	273	9	282

Error

Counts

282 → 9

Alt Table

Status	Error	Program
	8.2b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
▶	6.1b	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (*.f64 x y))))
	29.3b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	10.6b	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 3)) (+.f64 1 (+.f64 (.f64 x y) (pow.f64 (.f64 x y) 2)))))
✓	0.5b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x))
	6.1b	(.f64 x (/.f64 1 (/.f64 (+.f64 1 (.f64 x y)) (-.f64 1 (pow.f64 (*.f64 x y) 2)))))
✓	1.4b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	8.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) x) (+.f64 1 (*.f64 x y)))

Compiler

Compiled 9419 to 5651 computations (40% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (pow.f64 (*.f64 x y) 2))
✓	0.1b	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (*.f64 x y))))
✓	0.3b	(pow.f64 (*.f64 x y) 2)
✓	5.8b	(/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (.f64 x y)))

series51.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

19.0ms	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (*.f64 x y))))
14.0ms	(/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (.f64 x y)))
10.0ms	(-.f64 1 (pow.f64 (*.f64 x y) 2))
7.0ms	(pow.f64 (*.f64 x y) 2)

rewrite171.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

998×	`prod-diff_binary64`
207×	`egg-rr`
116×	`add-sqr-sqrt_binary64`
115×	`log1p-expm1-u_binary64`
115×	`expm1-log1p-u_binary64`

Counts

4 → 207

Calls

4 calls:

162.0ms	(-.f64 1 (pow.f64 (*.f64 x y) 2))
162.0ms	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (*.f64 x y))))
162.0ms	(pow.f64 (*.f64 x y) 2)
162.0ms	(/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	58
1	245	34
2	3075	34
3	4956	34
0	0	0
1	0	0

simplify190.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

489×	`distribute-rgt-neg-in_binary64`
473×	`distribute-lft-neg-in_binary64`
430×	`sub-neg_binary64`
368×	`cancel-sign-sub-inv_binary64`
364×	`neg-sub0_binary64`

Counts

303 → 222

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	894
1	51	894
2	95	894
3	241	894
4	902	894
5	1915	894
6	2848	894
7	4036	894
8	4739	894
9	4975	894
10	4882	894

prune316.0ms (7.4%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	222	9	231

Error

Counts

231 → 9

Alt Table

Status	Error	Program
	8.2b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	6.1b	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) (+.f64 1 (*.f64 x y))))
	29.3b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	10.6b	(.f64 x (/.f64 (-.f64 1 (pow.f64 (.f64 x y) 3)) (+.f64 1 (+.f64 (.f64 x y) (pow.f64 (.f64 x y) 2)))))
✓	0.5b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x))
	6.1b	(.f64 x (/.f64 1 (/.f64 (+.f64 1 (.f64 x y)) (-.f64 1 (pow.f64 (*.f64 x y) 2)))))
✓	1.4b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	8.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) x) (+.f64 1 (*.f64 x y)))

Compiler

Compiled 9203 to 5398 computations (41.3% saved)

regimes124.0ms (2.9%)

Accuracy

Total 0.1b remaining (80.1%)

Threshold costs 0.1b (80.1%)

Counts

38 → 1

Compiler

Compiled 1542 to 1058 computations (31.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	25	10
3	31	10
4	35	10
5	36	10
6	35	10

end108.0ms (2.5%)

Compiler: Compiled 156 to 103 computations (34% saved)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Details

analyze78.0ms (1.8%)

sample719.0ms (16.8%)

simplify18.0ms (0.4%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series10.0ms (0.2%)

rewrite46.0ms (1.1%)

simplify191.0ms (4.5%)

prune47.0ms (1.1%)

localize6.0ms (0.2%)

series1.3s (31.4%)

rewrite63.0ms (1.5%)

simplify80.0ms (1.9%)

prune139.0ms (3.3%)

localize7.0ms (0.2%)

series83.0ms (1.9%)

rewrite95.0ms (2.2%)

simplify123.0ms (2.9%)

prune257.0ms (6%)

localize7.0ms (0.2%)

series51.0ms (1.2%)

rewrite171.0ms (4%)

simplify190.0ms (4.4%)

prune316.0ms (7.4%)

regimes124.0ms (2.9%)

simplify3.0ms (0.1%)

end108.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10