Details

analyze775.0ms (23.2%)

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 (0.8%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify16.0ms (0.5%)

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 (0.1%)

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

2.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize16.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))

rewrite7.0ms (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:

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

series69.0ms (2.1%)

Counts

2 → 84

Calls

2 calls:

55.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
13.0ms	(-.f64 y (*.f64 z t))

simplify101.0ms (3%)

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

prune74.0ms (2.2%)

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

1.9b

Counts

220 → 6

Alt Table

Status	Error	Program
	45.4b	(.f64 (/.f64 x (-.f64 (pow.f64 y 3) (pow.f64 (.f64 z t) 3))) (+.f64 (.f64 y y) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 y (.f64 z t)))))
▶	2.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	2.8b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	30.5b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	2.8b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 1903 to 577 computations (69.7% saved)

localize6.0ms (0.2%)

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)))
✓	1.9b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

rewrite13.0ms (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:

7.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
3.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

series67.0ms (2%)

Counts

2 → 84

Calls

2 calls:

49.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
17.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify120.0ms (3.6%)

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 → 286

Iterations

Useful iterations: 2 (0.0ms)

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

prune132.0ms (4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	363	2	365
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	364	7	371

Error

1.9b

Counts

371 → 7

Alt Table

Status	Error	Program
✓	2.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
▶	2.8b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	30.5b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	32.8b	(.f64 (.f64 x (/.f64 1 (-.f64 (.f64 y y) (.f64 (.f64 z t) (.f64 z t))))) (+.f64 y (*.f64 z t)))
	2.8b	(.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))) (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))
	2.8b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 3419 to 1360 computations (60.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.8b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.0b	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite14.0ms (0.4%)

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

series96.0ms (2.9%)

Counts

2 → 96

Calls

2 calls:

49.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
47.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify143.0ms (4.3%)

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 → 378

Iterations

Useful iterations: 2 (0.0ms)

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

prune142.0ms (4.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	535	1	536
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	537	6	543

Error

1.9b

Counts

543 → 6

Alt Table

Status	Error	Program
✓	2.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	2.8b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	32.8b	(.f64 (.f64 x (/.f64 1 (-.f64 (.f64 y y) (.f64 (.f64 z t) (.f64 z t))))) (+.f64 y (*.f64 z t)))
▶	2.8b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
	2.8b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 4239 to 1341 computations (68.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.8b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
✓	2.1b	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))

rewrite25.0ms (0.8%)

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:

7.0ms	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))
6.0ms	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))

series103.0ms (3.1%)

Counts

2 → 96

Calls

2 calls:

56.0ms	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
46.0ms	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))

simplify122.0ms (3.6%)

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 → 333

Iterations

Useful iterations: 2 (0.0ms)

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

prune165.0ms (4.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	649	0	649
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	649	6	655

Error

1.9b

Counts

655 → 6

Alt Table

Status	Error	Program
✓	2.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	2.8b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	32.8b	(.f64 (.f64 x (/.f64 1 (-.f64 (.f64 y y) (.f64 (.f64 z t) (.f64 z t))))) (+.f64 y (*.f64 z t)))
✓	2.8b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
	2.8b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
✓	2.0b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 3400 to 1460 computations (57.1% saved)

regimes449.0ms (13.4%)

Accuracy

Total 0.1b remaining (2.6%)

Threshold costs 0.1b (2.6%)

Compiler

Compiled 10111 to 5815 computations (42.5% 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

end7.0ms (0.2%)

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

sample635.0ms (19%)

Algorithm

1×

intervals

Results

259.0ms	8000×	body	128	valid
12.0ms	368×	body	128	invalid

Compiler

Compiled 122 to 78 computations (36.1% 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

analyze775.0ms (23.2%)

sample28.0ms (0.8%)

simplify16.0ms (0.5%)

prune2.0ms (0.1%)

localize16.0ms (0.5%)

rewrite7.0ms (0.2%)

series69.0ms (2.1%)

simplify101.0ms (3%)

prune74.0ms (2.2%)

localize6.0ms (0.2%)

rewrite13.0ms (0.4%)

series67.0ms (2%)

simplify120.0ms (3.6%)

prune132.0ms (4%)

localize6.0ms (0.2%)

rewrite14.0ms (0.4%)

series96.0ms (2.9%)

simplify143.0ms (4.3%)

prune142.0ms (4.2%)

localize7.0ms (0.2%)

rewrite25.0ms (0.8%)

series103.0ms (3.1%)

simplify122.0ms (3.6%)

prune165.0ms (4.9%)

regimes449.0ms (13.4%)

simplify4.0ms (0.1%)

end7.0ms (0.2%)

sample635.0ms (19%)

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