Details

analyze407.0ms (15.2%)

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)

sample1.3s (49.3%)

Symmetry

(sort x y)

Results

897.0ms	8256×	body	128	valid
331.0ms	299×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify21.0ms (0.8%)

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)

series13.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

8.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
5.0ms	(.f64 (.f64 x 3) y)

rewrite13.0ms (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:

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

simplify78.0ms (2.9%)

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

prune41.0ms (1.5%)

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

0.0b

Counts

64 → 4

Alt Table

Status	Error	Program
	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))
	20.6b	(-.f64 (cbrt.f64 (pow.f64 (.f64 3 (.f64 y x)) 3)) z)
	0.4b	(-.f64 (.f64 x (.f64 3 y)) z)
▶	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)

Compiler

Compiled 910 to 532 computations (41.5% saved)

localize6.0ms (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))

series16.0ms (0.6%)

Counts

2 → 9

Calls

2 calls:

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

rewrite10.0ms (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:

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

simplify85.0ms (3.2%)

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

prune36.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	46	5	51

Error

0.0b

Counts

51 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))
	20.6b	(-.f64 (cbrt.f64 (pow.f64 (.f64 3 (.f64 y x)) 3)) z)
	0.4b	(-.f64 (.f64 x (.f64 3 y)) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
	0.3b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y x))) z)

Compiler

Compiled 742 to 410 computations (44.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(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))

simplify48.0ms (1.8%)

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

prune65.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	22	5	27

Error

0.0b

Counts

27 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))
	20.6b	(-.f64 (cbrt.f64 (pow.f64 (.f64 3 (.f64 y x)) 3)) z)
	0.4b	(-.f64 (.f64 x (.f64 3 y)) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
▶	0.3b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y x))) z)

Compiler

Compiled 340 to 203 computations (40.3% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y x))) z)
✓	0.3b	(.f64 (sqrt.f64 3) (.f64 y x))
✓	0.4b	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y x)))

series61.0ms (2.3%)

Counts

3 → 84

Calls

3 calls:

28.0ms	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y x))) z)
24.0ms	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y x)))
9.0ms	(.f64 (sqrt.f64 3) (.f64 y x))

rewrite26.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
12×	`associate-l_binary64`
9×	`*-un-lft-identity_binary64`

Counts

3 → 69

Calls

3 calls:

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

simplify101.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-def_binary64`
518×	`fma-neg_binary64`
386×	`*-commutative_binary64`
240×	`times-frac_binary64`
223×	`sqr-pow_binary64`

Counts

153 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1528
1	261	1455
2	911	1443
3	1787	1435
4	3811	1435
5	4843	1435
6	4883	1435

prune73.0ms (2.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	105	5	110

Error

Counts

110 → 5

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y x))) z)
	0.2b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y x)))) z)
✓	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))
	0.4b	(-.f64 (.f64 x (.f64 3 y)) z)
✓	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)

Compiler

Compiled 1812 to 1235 computations (31.8% saved)

regimes150.0ms (5.6%)

Accuracy

Total 0.1b remaining (95.7%)

Threshold costs 0.1b (95.7%)

Counts

19 → 1

Compiler

Compiled 1990 to 1481 computations (25.6% 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

end77.0ms (2.9%)

Remove: (sort x y)
Compiler: Compiled 107 to 80 computations (25.2% 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

analyze407.0ms (15.2%)

sample1.3s (49.3%)

simplify21.0ms (0.8%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series13.0ms (0.5%)

rewrite13.0ms (0.5%)

simplify78.0ms (2.9%)

prune41.0ms (1.5%)

localize6.0ms (0.2%)

series16.0ms (0.6%)

rewrite10.0ms (0.4%)

simplify85.0ms (3.2%)

prune36.0ms (1.3%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite1.0ms (0%)

simplify48.0ms (1.8%)

prune65.0ms (2.4%)

localize9.0ms (0.3%)

series61.0ms (2.3%)

rewrite26.0ms (1%)

simplify101.0ms (3.8%)

prune73.0ms (2.7%)

regimes150.0ms (5.6%)

simplify3.0ms (0.1%)

end77.0ms (2.9%)

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