Details

analyze586.0ms (14.9%)

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 (28.3%)

Symmetry

(sort z t)

Results

922.0ms	8256×	body	128	valid
37.0ms	338×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify18.0ms (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

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

1.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.0b	(/.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))
✓	1.0b	(/.f64 x (-.f64 y (*.f64 z t)))

series47.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

40.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
7.0ms	(-.f64 y (*.f64 z t))

rewrite8.0ms (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))

simplify88.0ms (2.2%)

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

prune82.0ms (2.1%)

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

0.9b

Counts

111 → 9

Alt Table

Status	Error	Program
	24.9b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
	1.9b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	31.4b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	29.3b	(/.f64 x y)
	33.1b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	25.4b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	1.9b	(.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)))))
▶	1.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	1.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))

Compiler

Compiled 2010 to 622 computations (69.1% 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)))
✓	0.9b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series58.0ms (1.5%)

Counts

2 → 84

Calls

2 calls:

38.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
20.0ms	(/.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:

7.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
4.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify101.0ms (2.6%)

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 → 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

prune135.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	183	9	192

Error

0.9b

Counts

192 → 9

Alt Table

Status	Error	Program
	24.9b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
	1.9b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	31.4b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	29.3b	(/.f64 x y)
	33.1b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	25.4b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	24.8b	(.f64 x (cbrt.f64 (pow.f64 (/.f64 1 (-.f64 y (.f64 t z))) 3)))
✓	1.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
▶	1.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))

Compiler

Compiled 3463 to 1390 computations (59.9% 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 (-.f64 y (*.f64 z t)) x))
✓	1.1b	(/.f64 (-.f64 y (*.f64 z t)) x)

series61.0ms (1.6%)

Counts

2 → 96

Calls

2 calls:

42.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
19.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite18.0ms (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:

5.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
4.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify128.0ms (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

prune171.0ms (4.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	224	11	235

Error

0.9b

Counts

235 → 11

Alt Table

Status	Error	Program
	24.9b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
	1.9b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
▶	1.2b	(/.f64 (/.f64 1 (-.f64 y (*.f64 z t))) (/.f64 1 x))
	31.4b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	29.3b	(/.f64 x y)
	33.1b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	2.2b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) x)) (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) x))) (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x))))
	25.4b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	24.8b	(.f64 x (cbrt.f64 (pow.f64 (/.f64 1 (-.f64 y (.f64 t z))) 3)))
✓	1.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	1.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))

Compiler

Compiled 4453 to 1450 computations (67.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
	0.4b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	1.0b	(/.f64 (/.f64 1 (-.f64 y (*.f64 z t))) (/.f64 1 x))

series41.0ms (1%)

Counts

1 → 48

Calls

1 calls:

41.0ms

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

rewrite50.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

465×	`times-frac_binary64`
211×	`*-un-lft-identity_binary64`
211×	`add-sqr-sqrt_binary64`
211×	`add-cube-cbrt_binary64`
41×	`add-exp-log_binary64`

Counts

1 → 257

Calls

1 calls:

12.0ms

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

simplify237.0ms (6%)

Algorithm

1×	egg-herbie

Rules

421×	`associate-*l/_binary64`
414×	`associate-/l/_binary64`
414×	`fma-def_binary64`
324×	`associate-/r/_binary64`
295×	`associate-*r/_binary64`

Counts

305 → 313

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	9019
1	566	8054
2	1943	7804
3	4729	7804
4	5011	7804

prune340.0ms (8.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	417	11	428

Error

0.9b

Counts

428 → 11

Alt Table

Status	Error	Program
	24.8b	(.f64 x (cbrt.f64 (pow.f64 (/.f64 1 (-.f64 y (.f64 t z))) 3)))
	1.9b	(/.f64 (.f64 (/.f64 (cbrt.f64 x) (-.f64 y (.f64 t z))) (cbrt.f64 x)) (/.f64 1 (cbrt.f64 x)))
✓	1.2b	(/.f64 (/.f64 1 (-.f64 y (*.f64 z t))) (/.f64 1 x))
	31.4b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	29.3b	(/.f64 x y)
	33.1b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	2.2b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) x)) (cbrt.f64 (/.f64 (-.f64 y (.f64 z t)) x))) (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x))))
	25.4b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	24.9b	(/.f64 x (cbrt.f64 (pow.f64 (-.f64 y (*.f64 t z)) 3)))
✓	1.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	1.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))

Compiler

Compiled 10477 to 4940 computations (52.8% saved)

regimes469.0ms (11.9%)

Accuracy

Total 0.1b remaining (2.6%)

Threshold costs 0.1b (2.6%)

Counts

72 → 1

Compiler

Compiled 9033 to 5382 computations (40.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-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	10	10
1	19	10
2	28	10
3	34	10
4	38	10
5	39	10
6	38	10

end133.0ms (3.4%)

Remove: (sort z t)
Compiler: Compiled 231 to 137 computations (40.7% 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

analyze586.0ms (14.9%)

sample1.1s (28.3%)

simplify18.0ms (0.5%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series47.0ms (1.2%)

rewrite8.0ms (0.2%)

simplify88.0ms (2.2%)

prune82.0ms (2.1%)

localize6.0ms (0.2%)

series58.0ms (1.5%)

rewrite15.0ms (0.4%)

simplify101.0ms (2.6%)

prune135.0ms (3.4%)

localize6.0ms (0.2%)

series61.0ms (1.6%)

rewrite18.0ms (0.5%)

simplify128.0ms (3.3%)

prune171.0ms (4.4%)

localize7.0ms (0.2%)

series41.0ms (1%)

rewrite50.0ms (1.3%)

simplify237.0ms (6%)

prune340.0ms (8.7%)

regimes469.0ms (11.9%)

simplify3.0ms (0.1%)

end133.0ms (3.4%)

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