Details

analyze461.0ms (12.7%)

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
37.4%	62.4%	0.2%	5
37.4%	62.4%	0.2%	6
43.7%	56.1%	0.2%	7
43.7%	56.1%	0.2%	8
51.5%	48.3%	0.2%	9
51.5%	48.3%	0.2%	10
56.9%	42.9%	0.2%	11
62%	37.8%	0.2%	12
70.4%	29.4%	0.2%	13
70.4%	29.4%	0.2%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (29.3%)

Symmetry

(sort z t)

Results

895.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

100×	`fma-def_binary64`
56×	`fma-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

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

2.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))

series50.0ms (1.4%)

Counts

2 → 84

Calls

2 calls:

43.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
7.0ms	(-.f64 y (*.f64 z t))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 51

Calls

2 calls:

4.0ms	(-.f64 y (*.f64 z t))
3.0ms	(/.f64 x (-.f64 y (*.f64 z t)))

simplify96.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

761×	`associate-/l*_binary64`
527×	`associate-/r*_binary64`
388×	`fma-def_binary64`
188×	`fma-neg_binary64`
173×	`associate-*l/_binary64`

Counts

135 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2389
1	332	2275
2	1159	2114
3	4821	2114
4	4954	2114

prune121.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	7	111

Error

2.8b

Counts

111 → 7

Alt Table

Status	Error	Program
	26.7b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	27.2b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
▶	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	3.3b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	3.7b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t)))))

Compiler

Compiled 1927 to 579 computations (70% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.2b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series63.0ms (1.7%)

Counts

2 → 84

Calls

2 calls:

40.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
23.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

2 → 75

Calls

2 calls:

7.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
5.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify118.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/r*_binary64`
540×	`fma-def_binary64`
347×	`associate-*l/_binary64`
222×	`fma-neg_binary64`
200×	`associate-/l/_binary64`

Counts

159 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	3528
1	394	3335
2	1569	3102
3	4897	3102
4	5060	3102

prune168.0ms (4.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	183	7	190

Error

2.8b

Counts

190 → 7

Alt Table

Status	Error	Program
	26.7b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	27.2b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
▶	3.3b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	3.7b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t)))))

Compiler

Compiled 3408 to 1343 computations (60.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.9b	(/.f64 (-.f64 y (*.f64 z t)) x)

series55.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

38.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
17.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 110

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
5.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify219.0ms (6%)

Algorithm

1×	egg-herbie

Rules

794×	`associate-/l*_binary64`
526×	`associate-/r*_binary64`
409×	`fma-def_binary64`
329×	`associate-/r/_binary64`
251×	`associate-/l/_binary64`

Counts

206 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	4158
1	402	3845
2	1455	3696
3	4932	3696
4	5008	3696

prune262.0ms (7.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	226	7	233

Error

2.8b

Counts

233 → 7

Alt Table

Status	Error	Program
	26.7b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	27.2b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
▶	3.4b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	3.3b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))

Compiler

Compiled 4282 to 1359 computations (68.3% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.5b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
✓	3.0b	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))

series71.0ms (2%)

Counts

2 → 96

Calls

2 calls:

40.0ms	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
29.0ms	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`div-exp_binary64`
16×	`add-cbrt-cube_binary64`
16×	`prod-exp_binary64`

Counts

2 → 88

Calls

2 calls:

9.0ms	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))
8.0ms	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))

simplify100.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

677×	`associate-/r*_binary64`
458×	`fma-def_binary64`
254×	`distribute-rgt-in_binary64`
226×	`distribute-lft-in_binary64`
208×	`associate-/r/_binary64`

Counts

184 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	3193
1	415	2878
2	1660	2734
3	4949	2734
4	5087	2734

prune138.0ms (3.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	189	7	196

Error

2.8b

Counts

196 → 7

Alt Table

Status	Error	Program
	26.7b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	27.2b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	3.4b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	3.3b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))

Compiler

Compiled 3430 to 1473 computations (57.1% saved)

regimes408.0ms (11.2%)

Accuracy

Total 0.1b remaining (2.3%)

Threshold costs 0.1b (2.3%)

Counts

58 → 1

Compiler

Compiled 7416 to 4261 computations (42.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`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	14	10
2	24	10
3	30	10
4	34	10
5	35	10
6	35	10

end108.0ms (3%)

Remove: (sort z t)
Compiler: Compiled 149 to 93 computations (37.6% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Details

analyze461.0ms (12.7%)

sample1.1s (29.3%)

simplify14.0ms (0.4%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series50.0ms (1.4%)

rewrite11.0ms (0.3%)

simplify96.0ms (2.6%)

prune121.0ms (3.3%)

localize6.0ms (0.2%)

series63.0ms (1.7%)

rewrite17.0ms (0.5%)

simplify118.0ms (3.3%)

prune168.0ms (4.6%)

localize7.0ms (0.2%)

series55.0ms (1.5%)

rewrite19.0ms (0.5%)

simplify219.0ms (6%)

prune262.0ms (7.2%)

localize16.0ms (0.4%)

series71.0ms (2%)

rewrite25.0ms (0.7%)

simplify100.0ms (2.8%)

prune138.0ms (3.8%)

regimes408.0ms (11.2%)

simplify5.0ms (0.1%)

end108.0ms (3%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10