Details

analyze606.0ms (14.2%)

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)

sample1.2s (27.8%)

Symmetry

(sort z t)

Results

984.0ms	8256×	body	128	valid
37.0ms	360×	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

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

2.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.1b	(/.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))
✓	2.1b	(/.f64 x (-.f64 y (*.f64 z t)))

series40.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

35.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
5.0ms	(-.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))

simplify84.0ms (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

prune70.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	7	111

Error

2.0b

Counts

111 → 7

Alt Table

Status	Error	Program
	33.2b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	25.7b	(cbrt.f64 (.f64 (.f64 (/.f64 x (-.f64 y (.f64 z t))) (/.f64 x (-.f64 y (.f64 z t)))) (/.f64 x (-.f64 y (*.f64 z t)))))
▶	2.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	31.3b	(/.f64 x y)
	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	2.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.1b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 1905 to 569 computations (70.1% saved)

localize9.0ms (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))
✓	1.9b	(/.f64 (-.f64 y (*.f64 z t)) x)

series54.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

37.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
17.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite22.0ms (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:

11.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
3.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify128.0ms (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%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	226	7	233

Error

2.0b

Counts

233 → 7

Alt Table

Status	Error	Program
	33.2b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	25.7b	(cbrt.f64 (.f64 (.f64 (/.f64 x (-.f64 y (.f64 z t))) (/.f64 x (-.f64 y (.f64 z t)))) (/.f64 x (-.f64 y (*.f64 z t)))))
▶	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	31.3b	(/.f64 x y)
	2.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.1b	(/.f64 x (-.f64 y (*.f64 z t)))
	33.4b	(/.f64 1 (.f64 (sqrt.f64 (/.f64 (-.f64 y (.f64 z t)) x)) (sqrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x))))

Compiler

Compiled 4328 to 1369 computations (68.4% saved)

localize8.0ms (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)))
✓	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series58.0ms (1.4%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
24.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite18.0ms (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))))
6.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify99.0ms (2.3%)

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

prune134.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	183	7	190

Error

2.0b

Counts

190 → 7

Alt Table

Status	Error	Program
	33.2b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	25.7b	(cbrt.f64 (.f64 (.f64 (/.f64 x (-.f64 y (.f64 z t))) (/.f64 x (-.f64 y (.f64 z t)))) (/.f64 x (-.f64 y (*.f64 z t)))))
✓	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	31.3b	(/.f64 x y)
▶	2.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.1b	(/.f64 x (-.f64 y (*.f64 z t)))
	33.4b	(/.f64 1 (.f64 (sqrt.f64 (/.f64 (-.f64 y (.f64 z t)) x)) (sqrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x))))

Compiler

Compiled 3406 to 1337 computations (60.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	0.9b	(/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))
✓	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))

series239.0ms (5.6%)

Counts

4 → 120

Calls

4 calls:

93.0ms	(/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))
64.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
39.0ms	(cbrt.f64 x)
38.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
41×	`cbrt-prod_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`

Counts

4 → 147

Calls

4 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
4.0ms	(/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))
1.0ms	(cbrt.f64 x)

simplify172.0ms (4%)

Algorithm

1×	egg-herbie

Rules

569×	`unswap-sqr_binary64`
473×	`cancel-sign-sub-inv_binary64`
435×	`associate-l_binary64`
298×	`associate-r_binary64`
213×	`times-frac_binary64`

Counts

267 → 243

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	5525
1	647	5072
2	3329	5004
3	3914	4941
4	5228	4941

prune176.0ms (4.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	278	8	286

Error

2.0b

Counts

286 → 8

Alt Table

Status	Error	Program
	33.2b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	25.7b	(cbrt.f64 (.f64 (.f64 (/.f64 x (-.f64 y (.f64 z t))) (/.f64 x (-.f64 y (.f64 z t)))) (/.f64 x (-.f64 y (*.f64 z t)))))
	3.2b	(.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (/.f64 (cbrt.f64 x) (-.f64 y (.f64 t z)))) (cbrt.f64 (/.f64 (cbrt.f64 x) (-.f64 y (.f64 t z)))))) (cbrt.f64 (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))))
✓	2.1b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	2.2b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	2.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	33.4b	(/.f64 1 (.f64 (sqrt.f64 (/.f64 (-.f64 y (.f64 z t)) x)) (sqrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x))))
	48.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 1 y) (pow.f64 x 1/3)))

Compiler

Compiled 6246 to 1430 computations (77.1% saved)

regimes805.0ms (18.9%)

Accuracy

Total 0.1b remaining (2.2%)

Threshold costs 0.1b (2.2%)

Counts

116 → 1

Compiler

Compiled 15340 to 9455 computations (38.4% 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

end108.0ms (2.5%)

Remove: (sort z t)
Compiler: Compiled 208 to 109 computations (47.6% 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

analyze606.0ms (14.2%)

sample1.2s (27.8%)

simplify16.0ms (0.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series40.0ms (0.9%)

rewrite7.0ms (0.2%)

simplify84.0ms (2%)

prune70.0ms (1.6%)

localize9.0ms (0.2%)

series54.0ms (1.3%)

rewrite22.0ms (0.5%)

simplify128.0ms (3%)

prune171.0ms (4%)

localize8.0ms (0.2%)

series58.0ms (1.4%)

rewrite18.0ms (0.4%)

simplify99.0ms (2.3%)

prune134.0ms (3.2%)

localize11.0ms (0.3%)

series239.0ms (5.6%)

rewrite30.0ms (0.7%)

simplify172.0ms (4%)

prune176.0ms (4.1%)

regimes805.0ms (18.9%)

simplify3.0ms (0.1%)

end108.0ms (2.5%)

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