Details

analyze610.0ms (16.4%)

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 (29.1%)

Symmetry

(sort z t)

Results

883.0ms	8256×	body	128	valid
46.0ms	368×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify16.0ms (0.4%)

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

2.0b

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)

localize5.0ms (0.1%)

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)))

series41.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

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

rewrite17.0ms (0.5%)

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

simplify78.0ms (2.1%)

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

prune128.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Error

1.9b

Counts

111 → 9

Alt Table

Status	Error	Program
	2.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	30.3b	(/.f64 x y)
	32.9b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	26.4b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
	2.8b	(/.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))))
	2.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
▶	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	30.2b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	21.1b	(/.f64 x (/.f64 (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y)) (fma.f64 t z y)))

Compiler

Compiled 2002 to 624 computations (68.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.3b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	2.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series54.0ms (1.4%)

Counts

2 → 84

Calls

2 calls:

36.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
18.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite15.0ms (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:

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

simplify106.0ms (2.8%)

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

prune137.0ms (3.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	183	9	192

Error

1.9b

Counts

192 → 9

Alt Table

Status	Error	Program
▶	2.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	30.3b	(/.f64 x y)
	32.9b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	26.4b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
	2.8b	(/.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))))
	2.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	30.2b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	21.1b	(/.f64 x (/.f64 (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y)) (fma.f64 t z y)))

Compiler

Compiled 3483 to 1388 computations (60.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.0b	(/.f64 (-.f64 y (*.f64 z t)) x)

series52.0ms (1.4%)

Counts

2 → 96

Calls

2 calls:

35.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
17.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite19.0ms (0.5%)

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:

6.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)
5.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))

simplify124.0ms (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

prune174.0ms (4.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	226	9	235

Error

1.9b

Counts

235 → 9

Alt Table

Status	Error	Program
✓	2.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	30.3b	(/.f64 x y)
	26.4b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
▶	2.2b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
	2.8b	(/.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))))
	2.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	3.0b	(.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))))
	30.2b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	21.1b	(/.f64 x (/.f64 (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y)) (fma.f64 t z y)))

Compiler

Compiled 4434 to 1425 computations (67.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.3b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
✓	2.2b	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))

series55.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

36.0ms	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
19.0ms	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))

rewrite21.0ms (0.6%)

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:

8.0ms	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
7.0ms	(.f64 (-.f64 y (.f64 z t)) (/.f64 1 x))

simplify99.0ms (2.7%)

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

prune136.0ms (3.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	189	9	198

Error

1.9b

Counts

198 → 9

Alt Table

Status	Error	Program
✓	2.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	30.3b	(/.f64 x y)
	26.4b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
✓	2.2b	(/.f64 1 (.f64 (-.f64 y (.f64 z t)) (/.f64 1 x)))
	2.8b	(/.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))))
	2.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	3.0b	(.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))))
	30.2b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	21.1b	(/.f64 x (/.f64 (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y)) (fma.f64 t z y)))

Compiler

Compiled 3494 to 1498 computations (57.1% saved)

regimes622.0ms (16.7%)

Accuracy

Total 0.1b remaining (2.2%)

Threshold costs 0.1b (2.2%)

Counts

84 → 1

Compiler

Compiled 11840 to 6676 computations (43.6% saved)

simplify3.0ms (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

end113.0ms (3%)

Remove: (sort z t)
Compiler: Compiled 213 to 118 computations (44.6% 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

analyze610.0ms (16.4%)

sample1.1s (29.1%)

simplify16.0ms (0.4%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series41.0ms (1.1%)

rewrite17.0ms (0.5%)

simplify78.0ms (2.1%)

prune128.0ms (3.4%)

localize6.0ms (0.2%)

series54.0ms (1.4%)

rewrite15.0ms (0.4%)

simplify106.0ms (2.8%)

prune137.0ms (3.7%)

localize7.0ms (0.2%)

series52.0ms (1.4%)

rewrite19.0ms (0.5%)

simplify124.0ms (3.3%)

prune174.0ms (4.7%)

localize7.0ms (0.2%)

series55.0ms (1.5%)

rewrite21.0ms (0.6%)

simplify99.0ms (2.7%)

prune136.0ms (3.6%)

regimes622.0ms (16.7%)

simplify3.0ms (0.1%)

end113.0ms (3%)

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