Details

analyze391.0ms (17.8%)

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
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)

sample889.0ms (40.5%)

Symmetry

(sort x y)

Results

788.0ms	8256×	body	128	valid
26.0ms	287×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify20.0ms (0.9%)

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

prune2.0ms (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 (0.2%)

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)

series16.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

11.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
5.0ms	(.f64 (.f64 x 3) y)

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

4.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
3.0ms	(.f64 (.f64 x 3) y)

simplify78.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-def_binary64`
637×	`fma-neg_binary64`
284×	`*-commutative_binary64`
255×	`unswap-sqr_binary64`
206×	`cancel-sign-sub-inv_binary64`

Counts

100 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	949
1	197	920
2	673	908
3	1389	908
4	2926	908
5	4712	908
6	4917	908

prune36.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	4	64

Error

Counts

64 → 4

Alt Table

Status	Error	Program
	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
	16.4b	(-.f64 (.f64 (.f64 (*.f64 x 3) (sqrt.f64 y)) (sqrt.f64 y)) z)
▶	0.1b	(-.f64 (.f64 x (.f64 3 y)) z)

Compiler

Compiled 902 to 523 computations (42% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series11.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

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

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

6.0ms	(-.f64 (.f64 x (.f64 3 y)) z)
3.0ms	(.f64 x (.f64 3 y))

simplify77.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
648×	`fma-neg_binary64`
275×	`*-commutative_binary64`
217×	`unswap-sqr_binary64`
215×	`times-frac_binary64`

Counts

100 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	947
1	188	918
2	650	906
3	1354	906
4	2928	906
5	4688	906
6	4904	906

prune33.0ms (1.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	63	4	67

Error

Counts

67 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
	16.4b	(-.f64 (.f64 (.f64 (*.f64 x 3) (sqrt.f64 y)) (sqrt.f64 y)) z)
✓	0.1b	(-.f64 (.f64 x (.f64 3 y)) z)

Compiler

Compiled 892 to 514 computations (42.4% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series12.0ms (0.5%)

Counts

2 → 9

Calls

2 calls:

6.0ms	(-.f64 (.f64 3 (.f64 y x)) z)
5.0ms	(.f64 3 (.f64 y x))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

4.0ms	(-.f64 (.f64 3 (.f64 y x)) z)
3.0ms	(.f64 3 (.f64 y x))

simplify79.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
659×	`fma-neg_binary64`
391×	`distribute-rgt-neg-in_binary64`
242×	`*-commutative_binary64`
211×	`unswap-sqr_binary64`

Counts

49 → 47

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	509
1	181	480
2	599	468
3	1237	468
4	2715	468
5	4443	468
6	4992	468
7	4832	468

prune26.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	47	4	51

Error

Counts

51 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
▶	16.4b	(-.f64 (.f64 (.f64 (*.f64 x 3) (sqrt.f64 y)) (sqrt.f64 y)) z)
✓	0.1b	(-.f64 (.f64 x (.f64 3 y)) z)

Compiler

Compiled 696 to 372 computations (46.6% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series31.0ms (1.4%)

Counts

3 → 64

Calls

3 calls:

13.0ms	(.f64 (.f64 x 3) (sqrt.f64 y))
10.0ms	(-.f64 (.f64 (.f64 (*.f64 x 3) (sqrt.f64 y)) (sqrt.f64 y)) z)
8.0ms	(.f64 (.f64 (*.f64 x 3) (sqrt.f64 y)) (sqrt.f64 y))

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
12×	`associate-r_binary64`
9×	`*-un-lft-identity_binary64`

Counts

3 → 69

Calls

3 calls:

7.0ms	(.f64 (.f64 (*.f64 x 3) (sqrt.f64 y)) (sqrt.f64 y))
6.0ms	(-.f64 (.f64 (.f64 (*.f64 x 3) (sqrt.f64 y)) (sqrt.f64 y)) z)
4.0ms	(.f64 (.f64 x 3) (sqrt.f64 y))

simplify106.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

763×	`fma-def_binary64`
604×	`fma-neg_binary64`
391×	`*-commutative_binary64`
261×	`associate-l_binary64`
222×	`sqr-pow_binary64`

Counts

133 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1350
1	272	1290
2	967	1278
3	1803	1278
4	3630	1278
5	4754	1278
6	4923	1278

prune53.0ms (2.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	103	4	107

Error

Counts

107 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
✓	16.4b	(-.f64 (.f64 (.f64 (*.f64 x 3) (sqrt.f64 y)) (sqrt.f64 y)) z)
✓	0.1b	(-.f64 (.f64 x (.f64 3 y)) z)

Compiler

Compiled 1767 to 856 computations (51.6% saved)

regimes64.0ms (2.9%)

Accuracy

Total 0.1b remaining (90.8%)

Threshold costs 0.1b (90.8%)

Counts

9 → 1

Compiler

Compiled 708 to 510 computations (28% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`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	12	10
2	17	10
3	19	10
4	20	10
5	20	10

end197.0ms (9%)

Compiler: Compiled 84 to 58 computations (31% 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	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

Details

analyze391.0ms (17.8%)

sample889.0ms (40.5%)

simplify20.0ms (0.9%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series16.0ms (0.7%)

rewrite9.0ms (0.4%)

simplify78.0ms (3.6%)

prune36.0ms (1.7%)

localize7.0ms (0.3%)

series11.0ms (0.5%)

rewrite11.0ms (0.5%)

simplify77.0ms (3.5%)

prune33.0ms (1.5%)

localize4.0ms (0.2%)

series12.0ms (0.5%)

rewrite9.0ms (0.4%)

simplify79.0ms (3.6%)

prune26.0ms (1.2%)

localize6.0ms (0.3%)

series31.0ms (1.4%)

rewrite21.0ms (0.9%)

simplify106.0ms (4.8%)

prune53.0ms (2.4%)

regimes64.0ms (2.9%)

simplify2.0ms (0.1%)

end197.0ms (9%)

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