Details

analyze590.0ms (11.4%)

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 (21.2%)

Symmetry

(sort z t)

Results

901.0ms	8256×	body	128	valid
41.0ms	347×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify15.0ms (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

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

3.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.6b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	3.6b	(/.f64 x (-.f64 y (*.f64 z t)))

series43.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

36.0ms	(/.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))

simplify84.0ms (1.6%)

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

prune76.0ms (1.5%)

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

3.5b

Counts

111 → 7

Alt Table

Status	Error	Program
✓	3.6b	(/.f64 x (-.f64 y (*.f64 z t)))
	26.3b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
	4.6b	(.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)))))
▶	3.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	4.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	30.0b	(/.f64 x y)
	34.3b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))

Compiler

Compiled 1917 to 573 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))
✓	0.5b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	3.4b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series56.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
22.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite13.0ms (0.3%)

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:

6.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
3.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify101.0ms (2%)

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

prune145.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	183	7	190

Error

3.5b

Counts

190 → 7

Alt Table

Status	Error	Program
	4.6b	(.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)))))
	30.1b	(*.f64 x (/.f64 1 y))
✓	3.6b	(/.f64 x (-.f64 y (*.f64 z t)))
	26.3b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
✓	3.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
▶	4.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	34.3b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))

Compiler

Compiled 3402 to 1341 computations (60.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.7b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	3.6b	(/.f64 (-.f64 y (*.f64 z t)) x)

series64.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

44.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
21.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite17.0ms (0.3%)

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

simplify126.0ms (2.4%)

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

prune153.0ms (3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	226	7	233

Error

3.5b

Counts

233 → 7

Alt Table

Status	Error	Program
▶	4.6b	(.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)))))
	30.1b	(*.f64 x (/.f64 1 y))
✓	3.6b	(/.f64 x (-.f64 y (*.f64 z t)))
	26.3b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
✓	3.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	4.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	34.3b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))

Compiler

Compiled 4298 to 1355 computations (68.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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)))))
✓	0.4b	(.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	3.6b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	14.8b	(cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t))))

series1.1s (21.9%)

Counts

3 → 144

Calls

3 calls:

667.0ms

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

418.0ms

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

49.0ms

(*.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)))))

rewrite62.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`cbrt-prod_binary64`
78×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 170

Calls

3 calls:

20.0ms

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

19.0ms

(*.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)))))

3.0ms

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

simplify189.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

691×	`times-frac_binary64`
505×	`associate-/r*_binary64`
428×	`associate-/l*_binary64`
310×	`fma-def_binary64`
224×	`*-commutative_binary64`

Counts

314 → 426

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	652	12128
1	1843	11619
2	5114	11619

prune571.0ms (11%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	872	0	872
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	872	7	879

Error

3.5b

Counts

879 → 7

Alt Table

Status	Error	Program
✓	4.6b	(.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)))))
	30.1b	(*.f64 x (/.f64 1 y))
✓	3.6b	(/.f64 x (-.f64 y (*.f64 z t)))
	26.3b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
✓	3.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	4.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	34.3b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))

Compiler

Compiled 37931 to 10359 computations (72.7% saved)

regimes513.0ms (9.9%)

Accuracy

Total 0.1b remaining (2.3%)

Threshold costs 0.1b (2.3%)

Counts

81 → 1

Compiler

Compiled 11840 to 6837 computations (42.3% saved)

simplify2.0ms (0%)

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

end83.0ms (1.6%)

Remove: (sort z t)
Compiler: Compiled 157 to 91 computations (42% 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

analyze590.0ms (11.4%)

sample1.1s (21.2%)

simplify15.0ms (0.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series43.0ms (0.8%)

rewrite8.0ms (0.2%)

simplify84.0ms (1.6%)

prune76.0ms (1.5%)

localize9.0ms (0.2%)

series56.0ms (1.1%)

rewrite13.0ms (0.3%)

simplify101.0ms (2%)

prune145.0ms (2.8%)

localize8.0ms (0.2%)

series64.0ms (1.2%)

rewrite17.0ms (0.3%)

simplify126.0ms (2.4%)

prune153.0ms (3%)

localize10.0ms (0.2%)

series1.1s (21.9%)

rewrite62.0ms (1.2%)

simplify189.0ms (3.7%)

prune571.0ms (11%)

regimes513.0ms (9.9%)

simplify2.0ms (0%)

end83.0ms (1.6%)

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