Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
99.8%	0%	0.2%	1

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample1.6s (50.9%)

Symmetry

(sort y z)

Results

1.3s	8251×	body	128	valid
1.0ms	3×	body	1024	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 53 to 41 computations (22.6% saved)

simplify53.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

382×	`fma-def_binary64`
322×	`fma-neg_binary64`
113×	`cancel-sign-sub-inv_binary64`
53×	`unsub-neg_binary64`
52×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	27	16
2	51	15
3	95	14
4	192	12
5	326	12
6	479	12
7	626	12
8	798	12
9	857	12
10	783	12

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize13.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))

series21.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

21.0ms

(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))

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:

1.0ms

(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))

simplify150.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

422×	`distribute-lft-in_binary64`
422×	`distribute-rgt-in_binary64`
368×	`distribute-lft-neg-out_binary64`
366×	`distribute-rgt-neg-out_binary64`
319×	`associate-l_binary64`

Counts

58 → 29

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	750
1	50	651
2	95	649
3	396	649
4	2320	649
5	4993	649
6	4952	649

prune57.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	2	30

Error

0.0b

Counts

30 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))
▶	37.1b	(cbrt.f64 (pow.f64 (fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t)) 3))

Compiler

Compiled 390 to 216 computations (44.6% saved)

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t))
✓	0.0b	(fma.f64 (*.f64 y z) -1/2 t)
✓	0.1b	(pow.f64 (fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t)) 3)
✓	37.1b	(cbrt.f64 (pow.f64 (fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t)) 3))

series215.0ms (6.8%)

Counts

4 → 180

Calls

4 calls:

127.0ms	(pow.f64 (fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t)) 3)
40.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t)) 3))
25.0ms	(fma.f64 (*.f64 y z) -1/2 t)
22.0ms	(fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

4 → 68

Calls

4 calls:

3.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t)) 3))
2.0ms	(pow.f64 (fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t)) 3)
0.0ms	(fma.f64 (*.f64 y z) -1/2 t)
0.0ms	(fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t))

simplify289.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

568×	`associate--r+_binary64`
245×	`unswap-sqr_binary64`
245×	`fma-neg_binary64`
244×	`sub-neg_binary64`
214×	`distribute-rgt-in_binary64`

Counts

248 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	6173
1	496	5615
2	1815	5456
3	4714	5456
4	5108	5456

prune143.0ms (4.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	139	2	141

Error

0.0b

Counts

141 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (*.f64 y z) -1/2 (fma.f64 1/8 x t))
✓	37.1b	(cbrt.f64 (pow.f64 (fma.f64 1/8 x (fma.f64 (*.f64 y z) -1/2 t)) 3))

Compiler

Compiled 3492 to 2155 computations (38.3% saved)

regimes455.0ms (14.5%)

Accuracy

Total -0.0b remaining (-559.9%)

Threshold costs -0.0b (-559.9%)

Counts

24 → 1

Compiler

Compiled 3336 to 2503 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
2	11	12

end108.0ms (3.4%)

Remove: (sort y z)
Compiler: Compiled 81 to 57 computations (29.6% saved)

Iter	Nodes	Cost
0	15	16
1	27	16
2	51	15
3	95	14
4	192	12
5	326	12
6	479	12
7	626	12
8	798	12
9	857	12
10	783	12

Iter	Nodes	Cost
0	15	16
1	27	16
2	51	15
3	95	14
4	192	12
5	326	12
6	479	12
7	626	12
8	798	12
9	857	12
10	783	12

Details

analyze4.0ms (0.1%)

sample1.6s (50.9%)

simplify53.0ms (1.7%)

prune5.0ms (0.2%)

localize13.0ms (0.4%)

series21.0ms (0.7%)

rewrite1.0ms (0%)

simplify150.0ms (4.8%)

prune57.0ms (1.8%)

localize18.0ms (0.6%)

series215.0ms (6.8%)

rewrite8.0ms (0.2%)

simplify289.0ms (9.2%)

prune143.0ms (4.5%)

regimes455.0ms (14.5%)

simplify4.0ms (0.1%)

end108.0ms (3.4%)

Profiling

Iter	Nodes	Cost
0	15	16
1	27	16
2	51	15
3	95	14
4	192	12
5	326	12
6	479	12
7	626	12
8	798	12
9	857	12
10	783	12