Details

analyze401.0ms (20.8%)

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)

sample838.0ms (43.4%)

Symmetry

(sort x y)

Results

743.0ms	8256×	body	128	valid
30.0ms	294×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify20.0ms (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

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

prune1.0ms (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)

series10.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

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

rewrite11.0ms (0.6%)

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:

5.0ms	(.f64 (.f64 x 3) y)
4.0ms	(-.f64 (.f64 (.f64 x 3) y) z)

simplify77.0ms (4%)

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

prune38.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	59	4	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	4	64

Error

Counts

64 → 4

Alt Table

Status	Error	Program
	0.5b	(-.f64 (.f64 (.f64 (.f64 x 3) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) z)
	0.4b	(-.f64 (.f64 x (.f64 3 y)) z)
	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
▶	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))

Compiler

Compiled 918 to 532 computations (42% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

6.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify45.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

908×	`unsub-neg_binary64`
729×	`distribute-rgt-in_binary64`
682×	`distribute-lft-in_binary64`
574×	`distribute-neg-out_binary64`
533×	`fma-neg_binary64`

Counts

46 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	468
1	37	447
2	61	447
3	210	447
4	863	447
5	2572	447
6	5078	447

prune12.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Error

Counts

26 → 4

Alt Table

Status	Error	Program
	0.5b	(-.f64 (.f64 (.f64 (.f64 x 3) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) z)
	0.4b	(-.f64 (.f64 x (.f64 3 y)) z)
▶	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))

Compiler

Compiled 330 to 188 computations (43% 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)
✓	0.3b	(.f64 3 (.f64 y x))

series10.0ms (0.5%)

Counts

2 → 9

Calls

2 calls:

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

rewrite9.0ms (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:

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

simplify78.0ms (4%)

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

prune31.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Error

Counts

51 → 4

Alt Table

Status	Error	Program
	0.5b	(-.f64 (.f64 (.f64 (.f64 x 3) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) z)
▶	0.4b	(-.f64 (.f64 x (.f64 3 y)) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))

Compiler

Compiled 712 to 381 computations (46.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x (.f64 3 y)) z)
✓	0.5b	(.f64 x (.f64 3 y))

series12.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

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

rewrite9.0ms (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:

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

simplify89.0ms (4.6%)

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

prune35.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

Counts

67 → 4

Alt Table

Status	Error	Program
	0.5b	(-.f64 (.f64 (.f64 (.f64 x 3) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) z)
✓	0.4b	(-.f64 (.f64 x (.f64 3 y)) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))

Compiler

Compiled 871 to 499 computations (42.7% saved)

regimes118.0ms (6.1%)

Accuracy

Total 0.1b remaining (90.3%)

Threshold costs 0.1b (90.3%)

Counts

17 → 1

Compiler

Compiled 1448 to 1057 computations (27% saved)

simplify2.0ms (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

end57.0ms (3%)

Remove: (sort x y)
Compiler: Compiled 87 to 59 computations (32.2% 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

analyze401.0ms (20.8%)

sample838.0ms (43.4%)

simplify20.0ms (1%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

series10.0ms (0.5%)

rewrite11.0ms (0.6%)

simplify77.0ms (4%)

prune38.0ms (2%)

localize5.0ms (0.3%)

series6.0ms (0.3%)

rewrite1.0ms (0%)

simplify45.0ms (2.3%)

prune12.0ms (0.6%)

localize4.0ms (0.2%)

series10.0ms (0.5%)

rewrite9.0ms (0.5%)

simplify78.0ms (4%)

prune31.0ms (1.6%)

localize5.0ms (0.2%)

series12.0ms (0.6%)

rewrite9.0ms (0.5%)

simplify89.0ms (4.6%)

prune35.0ms (1.8%)

regimes118.0ms (6.1%)

simplify2.0ms (0.1%)

end57.0ms (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