Details

analyze521.0ms (8.6%)

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
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)

sample158.0ms (2.6%)

Algorithm

1×

intervals

Symmetry

(sort z t)

Results

11.0ms	256×	body	128	valid
0.0ms	11×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify16.0ms (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

3.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.8b	(/.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))
✓	3.8b	(/.f64 x (-.f64 y (*.f64 z t)))

series44.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

38.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
6.0ms	(-.f64 y (*.f64 z t))

rewrite7.0ms (0.1%)

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:

3.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
2.0ms	(-.f64 y (*.f64 z t))

simplify82.0ms (1.4%)

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

prune80.0ms (1.3%)

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

3.7b

Counts

111 → 8

Alt Table

Status	Error	Program
	4.6b	(.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)))))
	28.0b	(/.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (*.f64 z t)))))
	32.6b	(/.f64 x y)
▶	3.9b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	4.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	3.8b	(/.f64 x (-.f64 y (*.f64 z t)))
	36.4b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
	4.6b	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))

Compiler

Compiled 1991 to 591 computations (70.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.5b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	3.5b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series60.0ms (1%)

Counts

2 → 84

Calls

2 calls:

41.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
18.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite15.0ms (0.2%)

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:

8.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
3.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify105.0ms (1.7%)

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

prune147.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

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

Error

3.7b

Counts

191 → 8

Alt Table

Status	Error	Program
	4.6b	(.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)))))
	28.0b	(/.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (*.f64 z t)))))
	32.6b	(/.f64 x y)
✓	3.9b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	4.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	3.8b	(/.f64 x (-.f64 y (*.f64 z t)))
	36.4b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
▶	4.6b	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))

Compiler

Compiled 3472 to 1355 computations (61% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))
✓	0.5b	(.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t))))
✓	0.6b	(/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
✓	9.9b	(cbrt.f64 (-.f64 y (*.f64 z t)))

series852.0ms (14.1%)

Counts

4 → 168

Calls

4 calls:

690.0ms	(/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
69.0ms	(.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t))))
53.0ms	(cbrt.f64 (-.f64 y (*.f64 z t)))
40.0ms	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))

rewrite69.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
112×	`cbrt-div_binary64`
69×	`add-sqr-sqrt_binary64`
67×	`cbrt-prod_binary64`
66×	`associate-/r/_binary64`

Counts

4 → 228

Calls

4 calls:

13.0ms	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))
8.0ms	(/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
6.0ms	(.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t))))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 z t)))

simplify269.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

754×	`associate-/r*_binary64`
562×	`associate-/l*_binary64`
388×	`fma-def_binary64`
271×	`associate-/l/_binary64`
212×	`*-commutative_binary64`

Counts

396 → 557

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	792	17961
1	2349	16978
2	5697	16978

prune574.0ms (9.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	716	1	717
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	716	9	725

Error

3.7b

Counts

725 → 9

Alt Table

Status	Error	Program
▶	4.6b	(.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)))))
	36.6b	(/.f64 (/.f64 x (.f64 (sqrt.f64 (cbrt.f64 (-.f64 y (.f64 z t)))) (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 y (.f64 t z)))) 3))) (cbrt.f64 (-.f64 y (.f64 z t))))
	28.0b	(/.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (*.f64 z t)))))
	32.6b	(/.f64 x y)
✓	3.9b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	4.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	3.8b	(/.f64 x (-.f64 y (*.f64 z t)))
	36.4b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
✓	4.6b	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))

Compiler

Compiled 31592 to 10282 computations (67.5% saved)

localize12.0ms (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)))))
	3.8b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	14.8b	(cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t))))

series1.1s (18.1%)

Counts

3 → 144

Calls

3 calls:

636.0ms

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

404.0ms

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

57.0ms

(*.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)))))

rewrite55.0ms (0.9%)

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)))))

14.0ms

(*.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))))

simplify197.0ms (3.3%)

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

prune642.0ms (10.6%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	872	0	872
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	872	9	881

Error

3.7b

Counts

881 → 9

Alt Table

Status	Error	Program
✓	4.6b	(.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)))))
	36.6b	(/.f64 (/.f64 x (.f64 (sqrt.f64 (cbrt.f64 (-.f64 y (.f64 z t)))) (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 y (.f64 t z)))) 3))) (cbrt.f64 (-.f64 y (.f64 z t))))
	28.0b	(/.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (*.f64 z t)))))
	32.6b	(/.f64 x y)
✓	3.9b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	4.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	3.8b	(/.f64 x (-.f64 y (*.f64 z t)))
	36.4b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
✓	4.6b	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))

Compiler

Compiled 37996 to 10383 computations (72.7% saved)

regimes350.0ms (5.8%)

Accuracy

Total 0.1b remaining (2.3%)

Threshold costs 0.1b (2.3%)

Counts

51 → 1

Compiler

Compiled 7633 to 4135 computations (45.8% saved)

simplify3.0ms (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

end5.0ms (0.1%)

Remove: (sort z t)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample678.0ms (11.2%)

Algorithm

1×

intervals

Results

287.0ms	8000×	body	128	valid
12.0ms	363×	body	128	invalid

Compiler

Compiled 205 to 106 computations (48.3% 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

analyze521.0ms (8.6%)

sample158.0ms (2.6%)

simplify16.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series44.0ms (0.7%)

rewrite7.0ms (0.1%)

simplify82.0ms (1.4%)

prune80.0ms (1.3%)

localize7.0ms (0.1%)

series60.0ms (1%)

rewrite15.0ms (0.2%)

simplify105.0ms (1.7%)

prune147.0ms (2.4%)

localize10.0ms (0.2%)

series852.0ms (14.1%)

rewrite69.0ms (1.1%)

simplify269.0ms (4.4%)

prune574.0ms (9.5%)

localize12.0ms (0.2%)

series1.1s (18.1%)

rewrite55.0ms (0.9%)

simplify197.0ms (3.3%)

prune642.0ms (10.6%)

regimes350.0ms (5.8%)

simplify3.0ms (0%)

end5.0ms (0.1%)

sample678.0ms (11.2%)

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