Details

analyze675.0ms (13.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
49.1%	50.7%	0.2%	9
49.5%	50.3%	0.2%	10
49.7%	50.1%	0.2%	11
50.2%	49.6%	0.2%	12
60.5%	39.3%	0.2%	13
60.6%	37.9%	1.4%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.4s (27.7%)

Symmetry

(sort x y)

Results

978.0ms	8256×	body	128	valid
331.0ms	2864×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify162.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1491×	`fma-neg_binary64`
579×	`fma-def_binary64`
465×	`distribute-rgt-in_binary64`
419×	`div-sub_binary64`
329×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	45	13
3	70	13
4	138	13
5	257	13
6	498	13
7	922	13
8	1615	13
9	2472	13
10	2435	13
11	2431	13
12	2427	13
13	2428	13
14	2428	13
15	3596	13
16	3260	13
17	3260	13
18	3260	13
19	3140	13

prune2.0ms (0%)

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

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series23.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

22.0ms

(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-/l*_binary64`
6×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

1 → 32

Calls

1 calls:

10.0ms

(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

429×	`div-sub_binary64`
352×	`distribute-rgt-in_binary64`
333×	`distribute-lft-in_binary64`
268×	`neg-mul-1_binary64`
200×	`associate-/l*_binary64`

Counts

80 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1540
1	274	1260
2	889	1216
3	3171	1099
4	4711	1099
5	5041	1099

prune37.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	3	62

Error

0.0b

Counts

62 → 3

Alt Table

Status	Error	Program
	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
▶	0.3b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))

Compiler

Compiled 1015 to 428 computations (57.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/2 (/.f64 x t))
✓	0.0b	(+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t)))
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
✓	0.2b	(*.f64 1/2 (/.f64 y t))

series63.0ms (1.2%)

Counts

4 → 66

Calls

4 calls:

33.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
16.0ms	(+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t)))
7.0ms	(*.f64 1/2 (/.f64 y t))
6.0ms	(*.f64 1/2 (/.f64 x t))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
26×	`associate-r_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`

Counts

4 → 112

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
5.0ms	(*.f64 1/2 (/.f64 y t))
5.0ms	(*.f64 1/2 (/.f64 x t))
4.0ms	(+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t)))

simplify147.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-def_binary64`
335×	`distribute-rgt-in_binary64`
314×	`distribute-lft-in_binary64`
270×	`associate-/l*_binary64`
262×	`fma-neg_binary64`

Counts

178 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	2804
1	555	2600
2	1797	2529
3	4756	2525
4	4989	2525
5	4994	2525
6	4945	2525

prune144.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	170	4	174

Error

Counts

174 → 4

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
	0.7b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 (.f64 (cbrt.f64 (.f64 1/2 (/.f64 y t))) (cbrt.f64 (.f64 1/2 (/.f64 y t)))) (cbrt.f64 (.f64 1/2 (/.f64 y t))))) (*.f64 1/2 (/.f64 z t)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
✓	0.3b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))

Compiler

Compiled 4286 to 2066 computations (51.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))

series24.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

23.0ms

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

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 41

Calls

1 calls:

10.0ms

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

simplify89.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-l_binary64`
427×	`associate-r_binary64`
356×	`div-sub_binary64`
350×	`associate-*r/_binary64`
340×	`associate-*l/_binary64`

Counts

89 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1760
1	327	1464
2	1329	1288
3	3680	1288
4	4980	1288
5	5099	1288

prune46.0ms (0.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	81	4	85

Error

Counts

85 → 4

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
▶	0.7b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 (.f64 (cbrt.f64 (.f64 1/2 (/.f64 y t))) (cbrt.f64 (.f64 1/2 (/.f64 y t)))) (cbrt.f64 (.f64 1/2 (/.f64 y t))))) (*.f64 1/2 (/.f64 z t)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
✓	0.3b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))

Compiler

Compiled 1463 to 645 computations (55.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 1/2 (/.f64 y t))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 1/2 (/.f64 y t))) (cbrt.f64 (.f64 1/2 (/.f64 y t)))) (cbrt.f64 (*.f64 1/2 (/.f64 y t))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 1/2 (/.f64 y t))) (cbrt.f64 (*.f64 1/2 (/.f64 y t))))
✓	10.6b	(cbrt.f64 (*.f64 1/2 (/.f64 y t)))

series1.2s (22.7%)

Counts

3 → 72

Calls

3 calls:

697.0ms

(*.f64 (cbrt.f64 (*.f64 1/2 (/.f64 y t))) (cbrt.f64 (*.f64 1/2 (/.f64 y t))))

421.0ms

(cbrt.f64 (*.f64 1/2 (/.f64 y t)))

56.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (/.f64 y t))) (cbrt.f64 (*.f64 1/2 (/.f64 y t)))) (cbrt.f64 (*.f64 1/2 (/.f64 y t))))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
21×	`associate-*r/_binary64`
17×	`cbrt-div_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`

Counts

3 → 90

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 1/2 (/.f64 y t))) (cbrt.f64 (*.f64 1/2 (/.f64 y t)))) (cbrt.f64 (*.f64 1/2 (/.f64 y t))))

4.0ms

(*.f64 (cbrt.f64 (*.f64 1/2 (/.f64 y t))) (cbrt.f64 (*.f64 1/2 (/.f64 y t))))

3.0ms

(cbrt.f64 (*.f64 1/2 (/.f64 y t)))

simplify119.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

480×	`fma-def_binary64`
300×	`unswap-sqr_binary64`
204×	`associate-*l/_binary64`
189×	`associate-*r/_binary64`
184×	`*-commutative_binary64`

Counts

162 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2725
1	310	2457
2	766	2133
3	2558	1904
4	4758	1904
5	4983	1904

prune300.0ms (5.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	288	4	292

Error

Counts

292 → 4

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
✓	0.7b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 (.f64 (cbrt.f64 (.f64 1/2 (/.f64 y t))) (cbrt.f64 (.f64 1/2 (/.f64 y t)))) (cbrt.f64 (.f64 1/2 (/.f64 y t))))) (*.f64 1/2 (/.f64 z t)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
✓	0.3b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))

Compiler

Compiled 10611 to 5870 computations (44.7% saved)

regimes458.0ms (8.9%)

Accuracy

Total 0.1b remaining (93.5%)

Threshold costs 0.1b (93.5%)

Counts

52 → 1

Compiler

Compiled 9288 to 6628 computations (28.6% saved)

simplify2.0ms (0%)

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	10	13
1	14	13
2	19	13
3	21	13
4	22	13
5	22	13

end79.0ms (1.5%)

Remove: (sort x y)
Compiler: Compiled 135 to 93 computations (31.1% saved)

Details

analyze675.0ms (13.1%)

sample1.4s (27.7%)

simplify162.0ms (3.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series23.0ms (0.4%)

rewrite11.0ms (0.2%)

simplify75.0ms (1.5%)

prune37.0ms (0.7%)

localize11.0ms (0.2%)

series63.0ms (1.2%)

rewrite31.0ms (0.6%)

simplify147.0ms (2.9%)

prune144.0ms (2.8%)

localize6.0ms (0.1%)

series24.0ms (0.5%)

rewrite13.0ms (0.3%)

simplify89.0ms (1.7%)

prune46.0ms (0.9%)

localize16.0ms (0.3%)

series1.2s (22.7%)

rewrite20.0ms (0.4%)

simplify119.0ms (2.3%)

prune300.0ms (5.8%)

regimes458.0ms (8.9%)

simplify2.0ms (0%)

end79.0ms (1.5%)

Profiling