Details

analyze661.0ms (17.6%)

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)

sample1.3s (35.5%)

Symmetry

(sort x y)

Results

890.0ms	8256×	body	128	valid
321.0ms	2867×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify156.0ms (4.2%)

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)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series21.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

20.0ms

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

rewrite9.0ms (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:

7.0ms

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

simplify74.0ms (2%)

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

prune42.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	3	62

Error

Counts

62 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (.f64 t 2))) (cbrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (.f64 t 2)))) (cbrt.f64 (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))))
	0.2b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))

Compiler

Compiled 1074 to 459 computations (57.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series60.0ms (1.6%)

Counts

4 → 66

Calls

4 calls:

31.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
17.0ms	(+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t)))
6.0ms	(*.f64 1/2 (/.f64 x t))
6.0ms	(*.f64 1/2 (/.f64 z t))

rewrite27.0ms (0.7%)

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:

6.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
6.0ms	(*.f64 1/2 (/.f64 x t))
4.0ms	(*.f64 1/2 (/.f64 z t))
4.0ms	(+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t)))

simplify113.0ms (3%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
336×	`distribute-rgt-in_binary64`
315×	`distribute-lft-in_binary64`
270×	`associate-/l*_binary64`
250×	`fma-neg_binary64`

Counts

178 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	2804
1	555	2600
2	1799	2529
3	4805	2525
4	4999	2525
5	4946	2525

prune119.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	172	3	175

Error

Counts

175 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
	25.3b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t))))
▶	0.2b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))

Compiler

Compiled 4272 to 2052 computations (52% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series21.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

21.0ms

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

rewrite12.0ms (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))

simplify81.0ms (2.2%)

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

prune53.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	81	3	84

Error

Counts

84 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
▶	25.3b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t))))
✓	0.2b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))

Compiler

Compiled 1432 to 622 computations (56.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t)))
	0.0b	(*.f64 1/2 (/.f64 x t))
✓	0.2b	(.f64 (.f64 1/2 (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t)))
✓	9.4b	(sqrt.f64 (/.f64 z t))

series33.0ms (0.9%)

Counts

2 → 16

Calls

2 calls:

17.0ms	(sqrt.f64 (/.f64 z t))
15.0ms	(.f64 (.f64 1/2 (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t)))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 63

Calls

2 calls:

10.0ms	(.f64 (.f64 1/2 (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t)))
2.0ms	(sqrt.f64 (/.f64 z t))

simplify86.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

570×	`associate-/l*_binary64`
508×	`associate-/r*_binary64`
385×	`unswap-sqr_binary64`
323×	`*-commutative_binary64`
300×	`associate-/l/_binary64`

Counts

79 → 88

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	958
1	207	882
2	604	881
3	1259	881
4	3067	866
5	3648	866
6	4638	866
7	5002	866

prune115.0ms (3.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	187	3	190

Error

Counts

190 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
✓	25.3b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t))))
✓	0.2b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))

Compiler

Compiled 5532 to 2254 computations (59.3% saved)

regimes613.0ms (16.3%)

Accuracy

Total 0.0b remaining (79.8%)

Threshold costs 0.0b (79.8%)

Counts

74 → 1

Compiler

Compiled 10352 to 7116 computations (31.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	19	13
2	23	13
3	25	13
4	26	13
5	25	13

end66.0ms (1.8%)

Remove: (sort x y)
Compiler: Compiled 113 to 77 computations (31.9% saved)

Details

analyze661.0ms (17.6%)

sample1.3s (35.5%)

simplify156.0ms (4.2%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series21.0ms (0.5%)

rewrite9.0ms (0.2%)

simplify74.0ms (2%)

prune42.0ms (1.1%)

localize11.0ms (0.3%)

series60.0ms (1.6%)

rewrite27.0ms (0.7%)

simplify113.0ms (3%)

prune119.0ms (3.2%)

localize6.0ms (0.2%)

series21.0ms (0.6%)

rewrite12.0ms (0.3%)

simplify81.0ms (2.2%)

prune53.0ms (1.4%)

localize13.0ms (0.3%)

series33.0ms (0.9%)

rewrite15.0ms (0.4%)

simplify86.0ms (2.3%)

prune115.0ms (3.1%)

regimes613.0ms (16.3%)

simplify2.0ms (0.1%)

end66.0ms (1.8%)

Profiling