Details

analyze73.0ms (3%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
25%	37.5%	37.6%	6
31.2%	31.2%	37.6%	7
37.5%	18.7%	43.8%	8
39%	15.6%	45.4%	9
42.1%	9.4%	48.5%	10
42.9%	7.8%	49.3%	11
44.5%	4.7%	50.8%	12
44.9%	3.9%	51.2%	13
45.7%	2.3%	52%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample851.0ms (34.9%)

Results

784.0ms	8256×	body	128	valid
20.0ms	226×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify17.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

151×	`fma-def_binary64`
131×	`fma-neg_binary64`
45×	`cancel-sign-sub-inv_binary64`
38×	`sub-neg_binary64`
31×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
▶	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 55 to 36 computations (34.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	0.2b	(*.f64 y (sqrt.f64 x))

series17.0ms (0.7%)

Counts

2 → 15

Calls

2 calls:

10.0ms	(*.f64 y (sqrt.f64 x))
8.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

rewrite53.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

903×	`log1p-expm1-u_binary64`
903×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
80×	`add-cbrt-cube_binary64`
80×	`add-log-exp_binary64`

Counts

2 → 54

Calls

2 calls:

52.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
52.0ms	(*.f64 y (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	173	16
2	2228	16
3	5435	16
0	0	0
1	0	0

simplify25.0ms (1%)

Algorithm

1×	egg-herbie

Rules

189×	`fma-def_binary64`
157×	`fma-neg_binary64`
52×	`cancel-sign-sub-inv_binary64`
34×	`associate--r+_binary64`
34×	`distribute-rgt-in_binary64`

Counts

69 → 61

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	113
1	23	113
2	34	113
3	52	113
4	80	113
5	130	113
6	223	113
7	300	113
8	353	113
9	394	113
10	408	113
11	414	113
12	383	113

prune52.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	58	5	63

Error

0.0b

Counts

63 → 5

Alt Table

Status	Error	Program
	17.1b	(fma.f64 (cbrt.f64 (.f64 x (.f64 y y))) (cbrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))
	31.1b	(+.f64 (-.f64 1 x) (pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) 2))
	29.4b	(.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (.f64 x (.f64 y y))) (/.f64 1 (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))))
	29.3b	(-.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))) (/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))))
▶	0.1b	(-.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))

Compiler

Compiled 1027 to 549 computations (46.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))
✓	0.0b	(-.f64 x (*.f64 y (sqrt.f64 x)))
	0.2b	(*.f64 y (sqrt.f64 x))

series18.0ms (0.7%)

Counts

2 → 20

Calls

2 calls:

10.0ms	(-.f64 x (*.f64 y (sqrt.f64 x)))
8.0ms	(-.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))

rewrite99.0ms (4.1%)

Algorithm

2×	batch-egg-rewrite

Rules

425×	`log-prod_binary64`
332×	`fma-def_binary64`
233×	`pow2_binary64`
192×	`egg-rr`
159×	`pow1/3_binary64`

Counts

2 → 192

Calls

2 calls:

94.0ms	(-.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))
94.0ms	(-.f64 x (*.f64 y (sqrt.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	177	21
2	2282	19
3	4973	19
4	4949	19
0	0	0
1	0	0

simplify29.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

201×	`fma-neg_binary64`
179×	`fma-def_binary64`
51×	`cancel-sign-sub-inv_binary64`
42×	`sub-neg_binary64`
30×	`associate--r+_binary64`

Counts

212 → 203

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	132
1	28	132
2	50	132
3	69	132
4	93	132
5	161	132
6	240	132
7	340	132
8	357	132
9	398	132
10	412	132
11	414	132
12	383	132

prune143.0ms (5.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	217	4	221

Error

Counts

221 → 4

Alt Table

Status	Error	Program
	31.2b	(-.f64 1 (fma.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (.f64 y (sqrt.f64 x)))) (-.f64 (sqrt.f64 x) (sqrt.f64 (.f64 y (sqrt.f64 x)))) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x)))))
	29.3b	(-.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))) (/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))))
✓	0.1b	(-.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))
▶	0.3b	(-.f64 1 (fma.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 x) y) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x)))))

Compiler

Compiled 3607 to 1357 computations (62.4% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (sqrt.f64 x) y)
	0.2b	(*.f64 y (sqrt.f64 x))
✓	0.4b	(fma.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 x) y) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x))))
✓	58.0b	(fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x)))

series191.0ms (7.9%)

Counts

3 → 40

Calls

3 calls:

156.0ms	(fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x)))
29.0ms	(fma.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 x) y) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x))))
6.0ms	(-.f64 (sqrt.f64 x) y)

rewrite52.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

810×	`log1p-expm1-u_binary64`
810×	`expm1-log1p-u_binary64`
153×	`log1p-udef_binary64`
98×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`

Counts

3 → 81

Calls

3 calls:

50.0ms	(-.f64 (sqrt.f64 x) y)
50.0ms	(fma.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 x) y) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x))))
50.0ms	(fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	45
1	192	35
2	2104	35
3	5111	35
0	0	0
1	0	0

simplify21.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

102×	`fma-def_binary64`
56×	`fma-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Counts

121 → 89

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	134
1	17	134
2	29	134
3	39	134
4	53	134
5	83	134
6	115	134
7	142	134
8	178	134
9	186	134
10	206	134
11	212	134
12	189	134

prune66.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	102	4	106

Error

Counts

106 → 4

Alt Table

Status	Error	Program
	31.2b	(-.f64 1 (fma.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (.f64 y (sqrt.f64 x)))) (-.f64 (sqrt.f64 x) (sqrt.f64 (.f64 y (sqrt.f64 x)))) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x)))))
▶	29.3b	(-.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))) (/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))))
✓	0.1b	(-.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))
✓	0.3b	(-.f64 1 (fma.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 x) y) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x)))))

Compiler

Compiled 2307 to 670 computations (71% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 x))
✓	6.8b	(.f64 x (.f64 y y))
✓	13.9b	(/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))))
✓	16.5b	(/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))))

series97.0ms (4%)

Counts

3 → 54

Calls

3 calls:

57.0ms	(/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))))
32.0ms	(/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))))
8.0ms	(.f64 x (.f64 y y))

rewrite100.0ms (4.1%)

Algorithm

2×	batch-egg-rewrite

Rules

266×	`fma-neg_binary64`
258×	`expm1-udef_binary64`
257×	`log1p-udef_binary64`
151×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`

Counts

3 → 99

Calls

3 calls:

98.0ms	(.f64 x (.f64 y y))
98.0ms	(/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))))
98.0ms	(/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	49
1	313	49
2	3998	49
3	4962	49
0	0	0
1	0	0

simplify73.0ms (3%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
336×	`times-frac_binary64`
259×	`associate-/r*_binary64`
250×	`associate-/l*_binary64`
237×	`fma-neg_binary64`

Counts

153 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	1735
1	449	1637
2	1625	1547
3	4875	1547
4	4982	1547

prune138.0ms (5.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	163	4	167

Error

Counts

167 → 4

Alt Table

Status	Error	Program
	31.2b	(-.f64 1 (fma.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (.f64 y (sqrt.f64 x)))) (-.f64 (sqrt.f64 x) (sqrt.f64 (.f64 y (sqrt.f64 x)))) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x)))))
✓	29.3b	(-.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))) (/.f64 (.f64 x (.f64 y y)) (-.f64 (-.f64 1 x) (.f64 y (sqrt.f64 x)))))
✓	0.1b	(-.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))
✓	0.3b	(-.f64 1 (fma.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 x) y) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 y (sqrt.f64 x)))))

Compiler

Compiled 6247 to 3300 computations (47.2% saved)

regimes222.0ms (9.1%)

Accuracy

Total 0.1b remaining (80.4%)

Threshold costs 0.1b (80.4%)

Counts

74 → 1

Compiler

Compiled 3695 to 2320 computations (37.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	15	10
3	17	10
4	18	10
5	17	10

end64.0ms (2.6%)

Compiler: Compiled 109 to 60 computations (45% saved)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Iter	Nodes	Cost
0	13	113
1	23	113
2	34	113
3	52	113
4	80	113
5	130	113
6	223	113
7	300	113
8	353	113
9	394	113
10	408	113
11	414	113
12	383	113

Iter	Nodes	Cost
0	14	132
1	28	132
2	50	132
3	69	132
4	93	132
5	161	132
6	240	132
7	340	132
8	357	132
9	398	132
10	412	132
11	414	132
12	383	132

Iter	Nodes	Cost
0	10	134
1	17	134
2	29	134
3	39	134
4	53	134
5	83	134
6	115	134
7	142	134
8	178	134
9	186	134
10	206	134
11	212	134
12	189	134

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Iter	Nodes	Cost
0	13	113
1	23	113
2	34	113
3	52	113
4	80	113
5	130	113
6	223	113
7	300	113
8	353	113
9	394	113
10	408	113
11	414	113
12	383	113

Iter	Nodes	Cost
0	14	132
1	28	132
2	50	132
3	69	132
4	93	132
5	161	132
6	240	132
7	340	132
8	357	132
9	398	132
10	412	132
11	414	132
12	383	132

Iter	Nodes	Cost
0	10	134
1	17	134
2	29	134
3	39	134
4	53	134
5	83	134
6	115	134
7	142	134
8	178	134
9	186	134
10	206	134
11	212	134
12	189	134

Details

analyze73.0ms (3%)

sample851.0ms (34.9%)

simplify17.0ms (0.7%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series17.0ms (0.7%)

rewrite53.0ms (2.2%)

simplify25.0ms (1%)

prune52.0ms (2.1%)

localize5.0ms (0.2%)

series18.0ms (0.7%)

rewrite99.0ms (4.1%)

simplify29.0ms (1.2%)

prune143.0ms (5.9%)

localize9.0ms (0.4%)

series191.0ms (7.9%)

rewrite52.0ms (2.1%)

simplify21.0ms (0.9%)

prune66.0ms (2.7%)

localize12.0ms (0.5%)

series97.0ms (4%)

rewrite100.0ms (4.1%)

simplify73.0ms (3%)

prune138.0ms (5.6%)

regimes222.0ms (9.1%)

simplify2.0ms (0.1%)

end64.0ms (2.6%)

Profiling

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Iter	Nodes	Cost
0	13	113
1	23	113
2	34	113
3	52	113
4	80	113
5	130	113
6	223	113
7	300	113
8	353	113
9	394	113
10	408	113
11	414	113
12	383	113

Iter	Nodes	Cost
0	14	132
1	28	132
2	50	132
3	69	132
4	93	132
5	161	132
6	240	132
7	340	132
8	357	132
9	398	132
10	412	132
11	414	132
12	383	132

Iter	Nodes	Cost
0	10	134
1	17	134
2	29	134
3	39	134
4	53	134
5	83	134
6	115	134
7	142	134
8	178	134
9	186	134
10	206	134
11	212	134
12	189	134