Details

analyze555.0ms (12.1%)

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
25%	74.9%	0.2%	7
25%	74.9%	0.2%	8
34.3%	65.5%	0.2%	9
39%	60.8%	0.2%	10
48.3%	51.5%	0.2%	11
53.7%	46.1%	0.2%	12
63.1%	36.7%	0.2%	13
64%	35.6%	0.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (23.5%)

Symmetry

(sort z t)

Results

883.0ms	8256×	body	128	valid
41.0ms	354×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify12.0ms (0.3%)

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

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

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)

localize5.0ms (0.1%)

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)))

series41.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

36.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
5.0ms	(-.f64 y (*.f64 z t))

rewrite9.0ms (0.2%)

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:

5.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
2.0ms	(-.f64 y (*.f64 z t))

simplify82.0ms (1.8%)

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

prune77.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	8	111

Error

2.8b

Counts

111 → 8

Alt Table

Status	Error	Program
	33.1b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (-.f64 y (.f64 z t)))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	3.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	32.9b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	3.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
	33.9b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	3.8b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
▶	3.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

Compiler

Compiled 2009 to 609 computations (69.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.4b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	2.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series46.0ms (1%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
14.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite20.0ms (0.4%)

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:

13.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
3.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify94.0ms (2.1%)

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

prune129.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	183	8	191

Error

2.8b

Counts

191 → 8

Alt Table

Status	Error	Program
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t)))))
▶	3.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	33.1b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (-.f64 y (.f64 z t)))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	33.9b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	3.8b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	29.8b	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))))
✓	3.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

Compiler

Compiled 3478 to 1379 computations (60.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.9b	(/.f64 (-.f64 y (*.f64 z t)) x)

series51.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

31.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
20.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite16.0ms (0.3%)

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

simplify123.0ms (2.7%)

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

prune158.0ms (3.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	227	7	234

Error

2.8b

Counts

234 → 7

Alt Table

Status	Error	Program
✓	3.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	33.9b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	4.2b	(/.f64 1 (/.f64 (/.f64 (-.f64 y (.f64 z t)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
▶	3.8b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	29.8b	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))))
✓	3.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

Compiler

Compiled 4322 to 1369 computations (68.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	0.4b	(.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	17.4b	(cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t))))

series839.0ms (18.3%)

Counts

3 → 144

Calls

3 calls:

478.0ms

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

311.0ms

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

49.0ms

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

rewrite49.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`cbrt-prod_binary64`
78×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 170

Calls

3 calls:

16.0ms

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

12.0ms

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

3.0ms

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

simplify187.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

691×	`times-frac_binary64`
505×	`associate-/r*_binary64`
428×	`associate-/l*_binary64`
310×	`fma-def_binary64`
224×	`*-commutative_binary64`

Counts

314 → 426

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	652	12128
1	1843	11619
2	5114	11619

prune609.0ms (13.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	872	0	872
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	872	7	879

Error

2.8b

Counts

879 → 7

Alt Table

Status	Error	Program
✓	3.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	33.9b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	4.2b	(/.f64 1 (/.f64 (/.f64 (-.f64 y (.f64 z t)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	3.8b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	29.8b	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))))
✓	3.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

Compiler

Compiled 37943 to 10366 computations (72.7% saved)

regimes290.0ms (6.3%)

Accuracy

Total 0.1b remaining (2.4%)

Threshold costs 0.1b (2.4%)

Counts

45 → 1

Compiler

Compiled 5925 to 3498 computations (41% saved)

simplify2.0ms (0%)

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

end87.0ms (1.9%)

Remove: (sort z t)
Compiler: Compiled 169 to 98 computations (42% 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

analyze555.0ms (12.1%)

sample1.1s (23.5%)

simplify12.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series41.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify82.0ms (1.8%)

prune77.0ms (1.7%)

localize6.0ms (0.1%)

series46.0ms (1%)

rewrite20.0ms (0.4%)

simplify94.0ms (2.1%)

prune129.0ms (2.8%)

localize6.0ms (0.1%)

series51.0ms (1.1%)

rewrite16.0ms (0.3%)

simplify123.0ms (2.7%)

prune158.0ms (3.4%)

localize9.0ms (0.2%)

series839.0ms (18.3%)

rewrite49.0ms (1.1%)

simplify187.0ms (4.1%)

prune609.0ms (13.3%)

regimes290.0ms (6.3%)

simplify2.0ms (0%)

end87.0ms (1.9%)

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