Details

analyze1.3s (13.6%)

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)

sample50.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify26.0ms (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

prune3.0ms (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

1.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.5b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	1.5b	(/.f64 x (-.f64 y (*.f64 z t)))

series86.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

75.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
10.0ms	(-.f64 y (*.f64 z t))

rewrite20.0ms (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:

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

simplify139.0ms (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

prune150.0ms (1.5%)

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

1.4b

Counts

111 → 8

Alt Table

Status	Error	Program
	25.4b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	1.5b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.5b	(/.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (*.f64 z t)))))
	34.0b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
	33.3b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	22.9b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
▶	1.8b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	2.3b	(.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)))))

Compiler

Compiled 2001 to 605 computations (69.8% saved)

localize12.0ms (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 (-.f64 y (*.f64 z t)) x))
✓	1.5b	(/.f64 (-.f64 y (*.f64 z t)) x)

series119.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

83.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
35.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite38.0ms (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:

11.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
9.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify321.0ms (3.3%)

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 → 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

prune343.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	223	3	226
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	228	6	234

Error

1.4b

Counts

234 → 6

Alt Table

Status	Error	Program
▶	1.7b	(/.f64 (/.f64 1 (-.f64 y (*.f64 z t))) (/.f64 1 x))
✓	1.5b	(/.f64 x (-.f64 y (*.f64 z t)))
	2.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (-.f64 y (.f64 t z)) x)) (cbrt.f64 (/.f64 (-.f64 y (.f64 t z)) x)))) (/.f64 1 (cbrt.f64 (/.f64 (-.f64 y (*.f64 t z)) x))))
	33.3b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	1.8b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
	2.3b	(.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)))))

Compiler

Compiled 4334 to 1375 computations (68.3% saved)

localize15.0ms (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)))
✓	1.6b	(/.f64 (/.f64 1 (-.f64 y (*.f64 z t))) (/.f64 1 x))

series119.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

78.0ms	(/.f64 (/.f64 1 (-.f64 y (*.f64 z t))) (/.f64 1 x))
40.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite115.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

474×	`times-frac_binary64`
220×	`*-un-lft-identity_binary64`
220×	`add-sqr-sqrt_binary64`
220×	`add-cube-cbrt_binary64`
46×	`add-exp-log_binary64`

Counts

2 → 292

Calls

2 calls:

23.0ms	(/.f64 (/.f64 1 (-.f64 y (*.f64 z t))) (/.f64 1 x))
7.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify490.0ms (5%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-def_binary64`
578×	`associate-*l/_binary64`
432×	`associate-/r/_binary64`
202×	`distribute-rgt-in_binary64`
159×	`distribute-lft-in_binary64`

Counts

376 → 379

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	10606
1	645	9567
2	2275	9230
3	5131	9230

prune715.0ms (7.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	418	5	423

Error

1.4b

Counts

423 → 5

Alt Table

Status	Error	Program
✓	1.5b	(/.f64 x (-.f64 y (*.f64 z t)))
	2.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (-.f64 y (.f64 t z)) x)) (cbrt.f64 (/.f64 (-.f64 y (.f64 t z)) x)))) (/.f64 1 (cbrt.f64 (/.f64 (-.f64 y (*.f64 t z)) x))))
	33.0b	(/.f64 (-.f64 (/.f64 -1 (.f64 t z)) (.f64 (+.f64 (/.f64 y (.f64 t z)) 1) (/.f64 y (.f64 (.f64 t z) (.f64 t z))))) (/.f64 1 x))
▶	1.8b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
	2.3b	(.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)))))

Compiler

Compiled 10517 to 4946 computations (53% saved)

localize28.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.4b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
✓	1.6b	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))

series111.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

74.0ms	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
37.0ms	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))

rewrite42.0ms (0.4%)

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:

15.0ms	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))
13.0ms	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))

simplify186.0ms (1.9%)

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

prune273.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	189	5	194

Error

1.4b

Counts

194 → 5

Alt Table

Status	Error	Program
✓	1.5b	(/.f64 x (-.f64 y (*.f64 z t)))
	2.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (-.f64 y (.f64 t z)) x)) (cbrt.f64 (/.f64 (-.f64 y (.f64 t z)) x)))) (/.f64 1 (cbrt.f64 (/.f64 (-.f64 y (*.f64 t z)) x))))
	33.0b	(/.f64 (-.f64 (/.f64 -1 (.f64 t z)) (.f64 (+.f64 (/.f64 y (.f64 t z)) 1) (/.f64 y (.f64 (.f64 t z) (.f64 t z))))) (/.f64 1 x))
✓	1.8b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
	2.3b	(.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)))))

Compiler

Compiled 3444 to 1469 computations (57.3% saved)

regimes3.9s (39.2%)

Accuracy

Total 0.0b remaining (1.6%)

Threshold costs 0.0b (1.6%)

Counts

274 → 1

Compiler

Compiled 41611 to 27746 computations (33.3% 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

end13.0ms (0.1%)

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

sample1.2s (12.4%)

Algorithm

1×

intervals

Results

546.0ms	8000×	body	128	valid
21.0ms	340×	body	128	invalid

Compiler

Compiled 146 to 80 computations (45.2% 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

analyze1.3s (13.6%)

sample50.0ms (0.5%)

simplify26.0ms (0.3%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series86.0ms (0.9%)

rewrite20.0ms (0.2%)

simplify139.0ms (1.4%)

prune150.0ms (1.5%)

localize12.0ms (0.1%)

series119.0ms (1.2%)

rewrite38.0ms (0.4%)

simplify321.0ms (3.3%)

prune343.0ms (3.5%)

localize15.0ms (0.2%)

series119.0ms (1.2%)

rewrite115.0ms (1.2%)

simplify490.0ms (5%)

prune715.0ms (7.3%)

localize28.0ms (0.3%)

series111.0ms (1.1%)

rewrite42.0ms (0.4%)

simplify186.0ms (1.9%)

prune273.0ms (2.8%)

regimes3.9s (39.2%)

simplify5.0ms (0.1%)

end13.0ms (0.1%)

sample1.2s (12.4%)

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