Details

analyze8.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
99.7%	0%	0.3%	1

Compiler

Compiled 25 to 18 computations (28% saved)

sample2.2s (54.2%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify187.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1251×	`fma-neg_binary64`
530×	`fma-def_binary64`
258×	`cancel-sign-sub-inv_binary64`
148×	`distribute-rgt-in_binary64`
135×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	23
1	34	23
2	77	22
3	156	21
4	332	19
5	674	19
6	959	19
7	1365	19
8	1815	19
9	1835	19
10	1845	19
11	1846	19
12	1846	19
13	2162	19
14	2166	19
15	2166	19
16	2055	19

prune7.0ms (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 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

Compiler

Compiled 80 to 51 computations (36.3% saved)

localize22.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
✓	0.0b	(fma.f64 (*.f64 a b) -1/4 c)

series123.0ms (3%)

Counts

3 → 180

Calls

3 calls:

70.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
39.0ms	(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
14.0ms	(fma.f64 (*.f64 a b) -1/4 c)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 30

Calls

3 calls:

0.0ms	(fma.f64 (*.f64 a b) -1/4 c)
0.0ms	(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
0.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

simplify258.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

560×	`distribute-lft-in_binary64`
560×	`distribute-rgt-in_binary64`
420×	`fma-def_binary64`
395×	`associate-l_binary64`
366×	`associate-r_binary64`

Counts

210 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	3513
1	112	3132
2	231	2908
3	780	2908
4	3702	2908
5	4969	2908
6	5000	2908
7	4953	2908

prune60.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	2	75

Error

0.0b

Counts

75 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
▶	22.7b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3))))

Compiler

Compiled 1440 to 716 computations (50.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3))))
✓	0.0b	(fma.f64 z (/.f64 t 16) (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3)))
✓	0.1b	(pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3)
✓	34.5b	(cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3))

series132.0ms (3.2%)

Counts

4 → 216

Calls

4 calls:

54.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3))))
40.0ms	(fma.f64 z (/.f64 t 16) (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3)))
28.0ms	(pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3)
10.0ms	(cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3))

rewrite7.0ms (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:

2.0ms	(cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3))
2.0ms	(pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3)
0.0ms	(fma.f64 z (/.f64 t 16) (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3)))
0.0ms	(fma.f64 x y (fma.f64 z (/.f64 t 16) (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3))))

simplify241.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
642×	`associate-l_binary64`
551×	`associate-r_binary64`
373×	`exp-prod_binary64`
285×	`fma-def_binary64`

Counts

284 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	5272
1	275	4771
2	752	4474
3	3533	4460
4	4960	4460
5	4928	4460

prune110.0ms (2.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	124	2	126

Error

0.0b

Counts

126 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
✓	22.7b	(fma.f64 x y (fma.f64 z (/.f64 t 16) (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 b -1/4) c) 3))))

Compiler

Compiled 2860 to 1710 computations (40.2% saved)

regimes508.0ms (12.3%)

Accuracy

Total 0.1b remaining (8.1%)

Threshold costs 0.1b (8.1%)

Counts

21 → 1

Compiler

Compiled 6745 to 4789 computations (29% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	16	19
2	16	19

end215.0ms (5.2%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 213 to 143 computations (32.9% saved)

Details

analyze8.0ms (0.2%)

sample2.2s (54.2%)

simplify187.0ms (4.5%)

prune7.0ms (0.2%)

localize22.0ms (0.5%)

series123.0ms (3%)

rewrite2.0ms (0%)

simplify258.0ms (6.2%)

prune60.0ms (1.4%)

localize14.0ms (0.3%)

series132.0ms (3.2%)

rewrite7.0ms (0.2%)

simplify241.0ms (5.8%)

prune110.0ms (2.7%)

regimes508.0ms (12.3%)

simplify4.0ms (0.1%)

end215.0ms (5.2%)

Profiling