Details

analyze437.0ms (13.6%)

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	62.4%	6.4%	9
46.8%	46.8%	6.4%	10
53.8%	39.8%	6.4%	11
57.3%	33.2%	9.5%	12
66.9%	23.6%	9.5%	13
70.3%	20.2%	9.5%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample842.0ms (26.1%)

Symmetry

(sort x y)

Results

749.0ms	8256×	body	128	valid
27.0ms	298×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify19.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

192×	`fma-def_binary64`
125×	`fma-neg_binary64`
44×	`distribute-rgt-neg-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
27×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

prune4.0ms (0.1%)

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 (.f64 x 3) y) z)

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x 3) y) z)
✓	0.2b	(.f64 (.f64 x 3) y)

series10.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

6.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
4.0ms	(.f64 (.f64 x 3) y)

rewrite63.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

832×	`expm1-log1p-u_binary64`
768×	`prod-diff_binary64`
132×	`egg-rr`
87×	`add-sqr-sqrt_binary64`
83×	`log1p-expm1-u_binary64`

Counts

2 → 132

Calls

2 calls:

60.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
60.0ms	(.f64 (.f64 x 3) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	172	17
2	2113	17
3	4986	17
0	0	0
1	0	0

simplify43.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

192×	`fma-def_binary64`
125×	`fma-neg_binary64`
44×	`distribute-rgt-neg-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
27×	`unsub-neg_binary64`

Counts

192 → 136

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	485
1	18	485
2	29	485
3	39	485
4	70	485
5	109	485
6	193	485
7	311	485
8	363	485
9	420	485
10	424	485
11	426	485
12	381	485

prune80.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	4	137

Error

0.0b

Counts

137 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (*.f64 3 y) (neg.f64 z))
	0.6b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)
	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)

Compiler

Compiled 2326 to 1094 computations (53% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (*.f64 3 y) (neg.f64 z))

series6.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

6.0ms

(fma.f64 x (*.f64 3 y) (neg.f64 z))

rewrite54.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

616×	`log1p-expm1-u_binary64`
616×	`expm1-log1p-u_binary64`
326×	`log-prod_binary64`
172×	`prod-diff_binary64`
130×	`expm1-udef_binary64`

Counts

1 → 91

Calls

1 calls:

50.0ms

(fma.f64 x (*.f64 3 y) (neg.f64 z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	162	8
2	1625	8
3	4977	8
0	0	0
1	0	0

simplify34.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

192×	`fma-def_binary64`
125×	`fma-neg_binary64`
44×	`distribute-rgt-neg-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
27×	`unsub-neg_binary64`

Counts

127 → 95

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	317
1	18	317
2	29	317
3	39	317
4	70	317
5	109	317
6	193	317
7	311	317
8	363	317
9	420	317
10	424	317
11	426	317
12	381	317

prune91.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	95	4	99

Error

0.0b

Counts

99 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (*.f64 3 y) (neg.f64 z))
	0.6b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)
▶	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)

Compiler

Compiled 2369 to 957 computations (59.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.3b	(.f64 3 (.f64 y x))

series10.0ms (0.3%)

Counts

2 → 9

Calls

2 calls:

6.0ms	(-.f64 (.f64 3 (.f64 y x)) z)
4.0ms	(.f64 3 (.f64 y x))

rewrite63.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

835×	`expm1-log1p-u_binary64`
729×	`prod-diff_binary64`
117×	`egg-rr`
87×	`add-sqr-sqrt_binary64`
83×	`log1p-expm1-u_binary64`

Counts

2 → 117

Calls

2 calls:

60.0ms	(-.f64 (.f64 3 (.f64 y x)) z)
60.0ms	(.f64 3 (.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	172	17
2	2120	17
3	4938	17
0	0	0
1	0	0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`sub-neg_binary64`
2×	`+-commutative_binary64`

Counts

126 → 119

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	47
1	15	47
2	23	47
3	24	47
4	26	47
5	30	47
6	31	47
7	36	47
8	31	47

prune57.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	119	4	123

Error

0.0b

Counts

123 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (*.f64 3 y) (neg.f64 z))
▶	0.6b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)

Compiler

Compiled 1978 to 826 computations (58.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)
	0.2b	(.f64 (.f64 x 3) y)
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3)
✓	8.3b	(cbrt.f64 (.f64 (.f64 x 3) y))

series730.0ms (22.7%)

Counts

3 → 84

Calls

3 calls:

359.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3)
323.0ms	(cbrt.f64 (.f64 (.f64 x 3) y))
47.0ms	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)

rewrite94.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

949×	`prod-diff_binary64`
376×	`fma-def_binary64`
271×	`fma-neg_binary64`
207×	`egg-rr`
173×	`expm1-udef_binary64`

Counts

3 → 207

Calls

3 calls:

89.0ms	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)
89.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3)
89.0ms	(cbrt.f64 (.f64 (.f64 x 3) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	199	26
2	2402	26
3	4649	26
4	4971	26
0	0	0
1	0	0

simplify81.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

424×	`unswap-sqr_binary64`
333×	`exp-prod_binary64`
270×	`associate-l_binary64`
268×	`distribute-neg-out_binary64`
229×	`unsub-neg_binary64`

Counts

291 → 225

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	55	1313
1	137	1313
2	238	1260
3	601	797
4	1901	781
5	4193	781
6	4940	781

prune132.0ms (4.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	240	4	244

Error

0.0b

Counts

244 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (*.f64 3 y) (neg.f64 z))
✓	0.6b	(-.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) 3) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)

Compiler

Compiled 3683 to 2338 computations (36.5% saved)

regimes135.0ms (4.2%)

Accuracy

Total 0.2b remaining (92.2%)

Threshold costs 0.2b (92.2%)

Counts

17 → 1

Compiler

Compiled 1582 to 1143 computations (27.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	13	10
2	15	10
3	16	10
4	16	10

end202.0ms (6.3%)

Compiler: Compiled 83 to 59 computations (28.9% saved)

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

Iter	Nodes	Cost
0	10	485
1	18	485
2	29	485
3	39	485
4	70	485
5	109	485
6	193	485
7	311	485
8	363	485
9	420	485
10	424	485
11	426	485
12	381	485

Iter	Nodes	Cost
0	10	317
1	18	317
2	29	317
3	39	317
4	70	317
5	109	317
6	193	317
7	311	317
8	363	317
9	420	317
10	424	317
11	426	317
12	381	317

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

Iter	Nodes	Cost
0	10	485
1	18	485
2	29	485
3	39	485
4	70	485
5	109	485
6	193	485
7	311	485
8	363	485
9	420	485
10	424	485
11	426	485
12	381	485

Iter	Nodes	Cost
0	10	317
1	18	317
2	29	317
3	39	317
4	70	317
5	109	317
6	193	317
7	311	317
8	363	317
9	420	317
10	424	317
11	426	317
12	381	317

Details

analyze437.0ms (13.6%)

sample842.0ms (26.1%)

simplify19.0ms (0.6%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series10.0ms (0.3%)

rewrite63.0ms (1.9%)

simplify43.0ms (1.3%)

prune80.0ms (2.5%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite54.0ms (1.7%)

simplify34.0ms (1.1%)

prune91.0ms (2.8%)

localize4.0ms (0.1%)

series10.0ms (0.3%)

rewrite63.0ms (1.9%)

simplify10.0ms (0.3%)

prune57.0ms (1.8%)

localize8.0ms (0.2%)

series730.0ms (22.7%)

rewrite94.0ms (2.9%)

simplify81.0ms (2.5%)

prune132.0ms (4.1%)

regimes135.0ms (4.2%)

simplify3.0ms (0.1%)

end202.0ms (6.3%)

Profiling

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

Iter	Nodes	Cost
0	10	485
1	18	485
2	29	485
3	39	485
4	70	485
5	109	485
6	193	485
7	311	485
8	363	485
9	420	485
10	424	485
11	426	485
12	381	485

Iter	Nodes	Cost
0	10	317
1	18	317
2	29	317
3	39	317
4	70	317
5	109	317
6	193	317
7	311	317
8	363	317
9	420	317
10	424	317
11	426	317
12	381	317