Details

analyze690.0ms (22.3%)

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
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
15.6%	80.3%	4.1%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample64.0ms (2.1%)

Algorithm

1×

intervals

Symmetry

(sort x y)

(sort z t)

Results

8.0ms	256×	body	128	valid
1.0ms	42×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify16.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

prune1.0ms (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 x y) (.f64 z t))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z t))

series9.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

9.0ms

(-.f64 (*.f64 x y) (*.f64 z t))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`cancel-sign-sub-inv_binary64`
1×	`flip--_binary64`
1×	`sub-neg_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 16

Calls

1 calls:

3.0ms

(-.f64 (*.f64 x y) (*.f64 z t))

simplify115.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

480×	`times-frac_binary64`
463×	`fma-def_binary64`
444×	`unsub-neg_binary64`
265×	`sub-neg_binary64`
232×	`distribute-rgt-neg-in_binary64`

Counts

64 → 32

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	682
1	113	658
2	347	652
3	974	652
4	2183	652
5	3451	652
6	4489	652
7	4961	652
8	4995	652
9	4859	652

prune20.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Error

Counts

33 → 3

Alt Table

Status	Error	Program
	35.9b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
	33.1b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
▶	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))

Compiler

Compiled 555 to 159 computations (71.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

9.0ms

(fma.f64 x y (neg.f64 (*.f64 z 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:

0.0ms

(fma.f64 x y (neg.f64 (*.f64 z t)))

simplify90.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

967×	`unsub-neg_binary64`
792×	`times-frac_binary64`
421×	`fma-neg_binary64`
384×	`neg-sub0_binary64`
364×	`neg-mul-1_binary64`

Counts

58 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	568
1	37	547
2	65	547
3	215	547
4	895	547
5	1760	547
6	3723	547
7	4512	547
8	5729	547

prune10.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Error

Counts

25 → 3

Alt Table

Status	Error	Program
	35.9b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
▶	33.1b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))

Compiler

Compiled 380 to 111 computations (70.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	0.2b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	0.8b	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

series110.0ms (3.5%)

Counts

2 → 56

Calls

2 calls:

67.0ms	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))
42.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
14×	`sqrt-div_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 78

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
3.0ms	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

simplify83.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

557×	`times-frac_binary64`
537×	`fma-neg_binary64`
342×	`*-commutative_binary64`
337×	`associate-/r*_binary64`
330×	`fma-def_binary64`

Counts

134 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	2631
1	335	2448
2	1184	2366
3	4373	2332
4	4960	2332

prune81.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	226	3	229

Error

Counts

229 → 3

Alt Table

Status	Error	Program
▶	35.9b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
✓	33.1b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))

Compiler

Compiled 6037 to 1074 computations (82.2% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t)))
✓	1.9b	(-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3))
✓	4.6b	(.f64 (.f64 x y) (*.f64 z t))
✓	34.9b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))

series267.0ms (8.6%)

Counts

4 → 192

Calls

4 calls:

154.0ms	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
65.0ms	(-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3))
32.0ms	(+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t)))
16.0ms	(.f64 (.f64 x y) (*.f64 z t))

rewrite60.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`prod-diff_binary64`
56×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
38×	`sqr-pow_binary64`
36×	`add-cube-cbrt_binary64`

Counts

4 → 196

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
7.0ms	(-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3))
6.0ms	(+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t)))
5.0ms	(.f64 (.f64 x y) (*.f64 z t))

simplify187.0ms (6%)

Algorithm

1×	egg-herbie

Rules

612×	`times-frac_binary64`
518×	`fma-neg_binary64`
396×	`associate-l_binary64`
370×	`associate-r_binary64`
247×	`exp-prod_binary64`

Counts

388 → 267

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	9918
1	623	8966
2	3184	8822
3	5004	8822

prune293.0ms (9.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	267	3	270

Error

Counts

270 → 3

Alt Table

Status	Error	Program
✓	35.9b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
✓	33.1b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))

Compiler

Compiled 14648 to 3755 computations (74.4% saved)

regimes239.0ms (7.7%)

Accuracy

Total 0.0b remaining (37.9%)

Threshold costs 0.0b (37.9%)

Counts

18 → 1

Compiler

Compiled 2591 to 1532 computations (40.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	25	10
3	30	10
4	32	10
5	32	10

end21.0ms (0.7%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 55 to 35 computations (36.4% saved)

sample671.0ms (21.7%)

Algorithm

1×

intervals

Results

257.0ms	8000×	body	128	valid
41.0ms	1374×	body	128	invalid

Compiler

Compiled 98 to 52 computations (46.9% saved)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Details

analyze690.0ms (22.3%)

sample64.0ms (2.1%)

simplify16.0ms (0.5%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite3.0ms (0.1%)

simplify115.0ms (3.7%)

prune20.0ms (0.7%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite1.0ms (0%)

simplify90.0ms (2.9%)

prune10.0ms (0.3%)

localize7.0ms (0.2%)

series110.0ms (3.5%)

rewrite20.0ms (0.6%)

simplify83.0ms (2.7%)

prune81.0ms (2.6%)

localize15.0ms (0.5%)

series267.0ms (8.6%)

rewrite60.0ms (1.9%)

simplify187.0ms (6%)

prune293.0ms (9.5%)

regimes239.0ms (7.7%)

simplify2.0ms (0.1%)

end21.0ms (0.7%)

sample671.0ms (21.7%)

Profiling

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10