Details

analyze430.0ms (14.5%)

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
21.8%	78%	0.1%	7
26.5%	73.3%	0.1%	8
36.7%	63.2%	0.1%	9
41.3%	49.9%	8.7%	10
47.2%	43.3%	9.5%	11
54.4%	35.5%	10.1%	12
57.9%	27.4%	14.7%	13
61.7%	23.2%	15.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample48.0ms (1.6%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

7.0ms	256×	body	128	valid
0.0ms	16×	body	128	invalid

Compiler

Compiled 24 to 18 computations (25% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def_binary64`
33×	`distribute-rgt-in_binary64`
26×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
21×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	45	10
3	88	10
4	170	10
5	254	10
6	256	10
7	258	10
8	252	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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))

series9.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(*.f64 (+.f64 x y) (+.f64 z 1))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`flip-+_binary64`
6×	`flip3-+_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`

Counts

1 → 32

Calls

1 calls:

6.0ms

(*.f64 (+.f64 x y) (+.f64 z 1))

simplify65.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

759×	`distribute-rgt-in_binary64`
724×	`distribute-lft-in_binary64`
449×	`fma-def_binary64`
414×	`fma-neg_binary64`
258×	`unsub-neg_binary64`

Counts

68 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	908
1	269	804
2	911	798
3	3385	798
4	4092	798
5	5126	798

prune46.0ms (1.5%)

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
	0.6b	(.f64 (.f64 (+.f64 x y) (*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))) (cbrt.f64 (+.f64 z 1)))
▶	0.0b	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
	14.4b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))

Compiler

Compiled 1000 to 519 computations (48.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 z x) x)
✓	0.0b	(+.f64 (.f64 y z) (+.f64 (.f64 z x) x))
✓	0.0b	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))

series20.0ms (0.7%)

Counts

3 → 33

Calls

3 calls:

10.0ms	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
7.0ms	(+.f64 (.f64 y z) (+.f64 (.f64 z x) x))
4.0ms	(+.f64 (*.f64 z x) x)

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
10×	`sum-log_binary64`
7×	`*-un-lft-identity_binary64`
5×	`fma-def_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 52

Calls

3 calls:

7.0ms	(+.f64 (.f64 y z) (+.f64 (.f64 z x) x))
7.0ms	(+.f64 y (+.f64 (.f64 y z) (+.f64 (.f64 z x) x)))
3.0ms	(+.f64 (*.f64 z x) x)

simplify59.0ms (2%)

Algorithm

1×	egg-herbie

Rules

661×	`distribute-rgt-in_binary64`
623×	`fma-def_binary64`
605×	`fma-neg_binary64`
593×	`distribute-lft-in_binary64`
396×	`associate-l_binary64`

Counts

85 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	839
1	270	770
2	983	748
3	4469	747
4	5002	747

prune47.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	95	2	97

Error

Counts

97 → 2

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (+.f64 x y) (*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))) (cbrt.f64 (+.f64 z 1)))
▶	0.0b	(+.f64 y (fma.f64 y z (+.f64 (*.f64 z x) x)))

Compiler

Compiled 1535 to 414 computations (73% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (*.f64 z x) x)
✓	0.0b	(+.f64 y (fma.f64 y z (+.f64 (*.f64 z x) x)))

series9.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(+.f64 y (fma.f64 y z (+.f64 (*.f64 z x) x)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

(+.f64 y (fma.f64 y z (+.f64 (*.f64 z x) x)))

simplify55.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

525×	`associate--l-_binary64`
496×	`sub-neg_binary64`
425×	`distribute-rgt-in_binary64`
413×	`distribute-lft-in_binary64`
349×	`associate--r+_binary64`

Counts

54 → 40

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	662
1	104	584
2	354	544
3	2036	544
4	3077	543
5	5217	543

prune28.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	65	2	67

Error

Counts

67 → 2

Alt Table

Status	Error	Program
▶	0.6b	(.f64 (.f64 (+.f64 x y) (*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))) (cbrt.f64 (+.f64 z 1)))
✓	0.0b	(+.f64 y (fma.f64 y z (+.f64 (*.f64 z x) x)))

Compiler

Compiled 981 to 307 computations (68.7% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 x y) (.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1))))
✓	0.2b	(.f64 (.f64 (+.f64 x y) (*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))) (cbrt.f64 (+.f64 z 1)))
✓	0.2b	(*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))
✓	0.2b	(cbrt.f64 (+.f64 z 1))

series226.0ms (7.6%)

Counts

4 → 96

Calls

4 calls:

206.0ms	(.f64 (+.f64 x y) (.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1))))
8.0ms	(.f64 (.f64 (+.f64 x y) (*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))) (cbrt.f64 (+.f64 z 1)))
7.0ms	(cbrt.f64 (+.f64 z 1))
5.0ms	(*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))

rewrite144.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Rules

212×	`cbrt-div_binary64`
168×	`frac-times_binary64`
142×	`flip-+_binary64`
142×	`flip3-+_binary64`
60×	`associate-*r/_binary64`

Counts

4 → 226

Calls

4 calls:

20.0ms	(.f64 (.f64 (+.f64 x y) (*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))) (cbrt.f64 (+.f64 z 1)))
11.0ms	(.f64 (+.f64 x y) (.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1))))
10.0ms	(*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))
2.0ms	(cbrt.f64 (+.f64 z 1))

simplify240.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

673×	`associate-l_binary64`
527×	`associate-r_binary64`
405×	`cancel-sign-sub-inv_binary64`
357×	`times-frac_binary64`
304×	`*-commutative_binary64`

Counts

322 → 405

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	420	9267
1	1055	8758
2	3366	8252
3	4462	8187
4	5148	8187

prune423.0ms (14.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	503	0	503
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	503	2	505

Error

Counts

505 → 2

Alt Table

Status	Error	Program
✓	0.6b	(.f64 (.f64 (+.f64 x y) (*.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (+.f64 z 1)))) (cbrt.f64 (+.f64 z 1)))
✓	0.0b	(+.f64 y (fma.f64 y z (+.f64 (*.f64 z x) x)))

Compiler

Compiled 16291 to 10821 computations (33.6% saved)

regimes478.0ms (16.2%)

Accuracy

Total 0.0b remaining (21.1%)

Threshold costs 0.0b (21.1%)

Counts

71 → 1

Compiler

Compiled 6939 to 4879 computations (29.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	11	14
2	11	14

end11.0ms (0.4%)

Remove: (sort x y)
Compiler: Compiled 39 to 21 computations (46.2% saved)

sample553.0ms (18.7%)

Algorithm

1×

intervals

Results

220.0ms	7996×	body	128	valid
19.0ms	558×	body	128	invalid
0.0ms	3×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 61 to 41 computations (32.8% saved)

Details

analyze430.0ms (14.5%)

sample48.0ms (1.6%)

simplify10.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite8.0ms (0.3%)

simplify65.0ms (2.2%)

prune46.0ms (1.5%)

localize7.0ms (0.2%)

series20.0ms (0.7%)

rewrite19.0ms (0.6%)

simplify59.0ms (2%)

prune47.0ms (1.6%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite3.0ms (0.1%)

simplify55.0ms (1.9%)

prune28.0ms (0.9%)

localize8.0ms (0.3%)

series226.0ms (7.6%)

rewrite144.0ms (4.9%)

simplify240.0ms (8.1%)

prune423.0ms (14.3%)

regimes478.0ms (16.2%)

simplify2.0ms (0.1%)

end11.0ms (0.4%)

sample553.0ms (18.7%)

Profiling