Details

analyze800.0ms (12%)

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)

sample28.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify16.0ms (0.2%)

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

4.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	4.1b	(/.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))
✓	4.1b	(/.f64 x (-.f64 y (*.f64 z t)))

rewrite8.0ms (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))

series71.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

58.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
13.0ms	(-.f64 y (*.f64 z t))

simplify100.0ms (1.5%)

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 → 219

Iterations

Useful iterations: 2 (0.0ms)

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

prune118.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	214	5	219
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	214	6	220

Error

4.0b

Counts

220 → 6

Alt Table

Status	Error	Program
✓	4.1b	(/.f64 x (-.f64 y (*.f64 z t)))
	5.0b	(/.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))))
	5.0b	(.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)))))
▶	4.9b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	28.7b	(/.f64 x y)
	35.6b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))

Compiler

Compiled 1911 to 557 computations (70.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 x)
✓	0.6b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	2.1b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
✓	2.3b	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`
49×	`cbrt-prod_binary64`

Counts

4 → 165

Calls

4 calls:

8.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
5.0ms	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

series1.1s (15.8%)

Counts

4 → 120

Calls

4 calls:

516.0ms	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
228.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
227.0ms	(cbrt.f64 x)
80.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))

simplify186.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-def_binary64`
412×	`unswap-sqr_binary64`
347×	`associate-/l*_binary64`
274×	`div-sub_binary64`
183×	`times-frac_binary64`

Counts

285 → 535

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	258	5914
1	632	5095
2	2949	4957
3	4109	4873
4	4977	4873

prune189.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	533	2	535
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	533	8	541

Error

4.0b

Counts

541 → 8

Alt Table

Status	Error	Program
✓	4.1b	(/.f64 x (-.f64 y (*.f64 z t)))
▶	5.0b	(/.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))))
	5.0b	(.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)))))
✓	4.9b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	28.7b	(/.f64 x y)
	5.1b	(.f64 (/.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x))) (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x))))) (/.f64 (cbrt.f64 x) (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x)))))
	35.6b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	46.7b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 y (pow.f64 (/.f64 1 x) 1/3)))

Compiler

Compiled 6748 to 1447 computations (78.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.5b	(/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
	10.8b	(cbrt.f64 (-.f64 y (*.f64 z t)))
	10.8b	(cbrt.f64 (-.f64 y (*.f64 z t)))
✓	10.8b	(cbrt.f64 (-.f64 y (*.f64 z t)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cbrt-div_binary64`
8×	`associate-/r/_binary64`
7×	`flip--_binary64`
7×	`flip3--_binary64`
7×	`add-exp-log_binary64`

Counts

2 → 46

Calls

2 calls:

11.0ms	(/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 z t)))

series788.0ms (11.8%)

Counts

2 → 84

Calls

2 calls:

735.0ms	(/.f64 x (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
52.0ms	(cbrt.f64 (-.f64 y (*.f64 z t)))

simplify157.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-def_binary64`
636×	`times-frac_binary64`
423×	`associate-/r*_binary64`
336×	`associate-/l*_binary64`
323×	`associate-l_binary64`

Counts

130 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	429	5731
1	1375	5460
2	4671	5380
3	5078	5380

prune304.0ms (4.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	538	2	540
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	540	8	548

Error

4.0b

Counts

548 → 8

Alt Table

Status	Error	Program
	35.8b	(/.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))
	28.7b	(/.f64 x y)
✓	4.1b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	4.9b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
▶	5.1b	(.f64 (/.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x))) (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x))))) (/.f64 (cbrt.f64 x) (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x)))))
	21.3b	(/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 y (.f64 t z)) 2))) x) (cbrt.f64 (-.f64 y (*.f64 z t))))
	35.6b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	46.7b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 y (pow.f64 (/.f64 1 x) 1/3)))

Compiler

Compiled 16092 to 6783 computations (57.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.3b	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
	12.0b	(cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x)))
	12.0b	(cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x)))
✓	12.0b	(cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`cbrt-prod_binary64`
18×	`times-frac_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`

Counts

1 → 33

Calls

1 calls:

3.0ms

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

series1.0s (15.1%)

Counts

1 → 48

Calls

1 calls:

1.0s	(cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x)))

simplify114.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

667×	`cancel-sign-sub-inv_binary64`
321×	`associate-r_binary64`
291×	`fma-neg_binary64`
290×	`unswap-sqr_binary64`
254×	`associate-l_binary64`

Counts

81 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	296	3849
1	875	3619
2	3403	3561
3	5416	3561

prune356.0ms (5.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	817	0	817
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	817	8	825

Error

4.0b

Counts

825 → 8

Alt Table

Status	Error	Program
	35.8b	(/.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))) (cbrt.f64 (-.f64 y (.f64 z t))))
	28.7b	(/.f64 x y)
✓	4.1b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	4.9b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
✓	5.1b	(.f64 (/.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x))) (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x))))) (/.f64 (cbrt.f64 x) (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x)))))
	21.3b	(/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (-.f64 y (.f64 t z)) 2))) x) (cbrt.f64 (-.f64 y (*.f64 z t))))
	35.6b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	46.7b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 y (pow.f64 (/.f64 1 x) 1/3)))

Compiler

Compiled 25205 to 7695 computations (69.5% saved)

regimes616.0ms (9.2%)

Accuracy

Total 0.0b remaining (1.5%)

Threshold costs 0.0b (1.5%)

Compiler

Compiled 11973 to 6396 computations (46.6% saved)

simplify4.0ms (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

end6.0ms (0.1%)

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

sample658.0ms (9.9%)

Algorithm

1×

intervals

Results

273.0ms	8000×	body	128	valid
10.0ms	323×	body	128	invalid

Compiler

Compiled 198 to 106 computations (46.5% 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

analyze800.0ms (12%)

sample28.0ms (0.4%)

simplify16.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite8.0ms (0.1%)

series71.0ms (1.1%)

simplify100.0ms (1.5%)

prune118.0ms (1.8%)

localize9.0ms (0.1%)

rewrite30.0ms (0.4%)

series1.1s (15.8%)

simplify186.0ms (2.8%)

prune189.0ms (2.8%)

localize9.0ms (0.1%)

rewrite16.0ms (0.2%)

series788.0ms (11.8%)

simplify157.0ms (2.4%)

prune304.0ms (4.6%)

localize15.0ms (0.2%)

rewrite6.0ms (0.1%)

series1.0s (15.1%)

simplify114.0ms (1.7%)

prune356.0ms (5.3%)

regimes616.0ms (9.2%)

simplify4.0ms (0.1%)

end6.0ms (0.1%)

sample658.0ms (9.9%)

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