Details

analyze1.3s (15.1%)

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)

sample46.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify29.0ms (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

2.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.6b	(/.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))
✓	2.7b	(/.f64 x (-.f64 y (*.f64 z t)))

series81.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

71.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
10.0ms	(-.f64 y (*.f64 z t))

rewrite16.0ms (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))

simplify174.0ms (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

prune180.0ms (2%)

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

2.5b

Counts

111 → 9

Alt Table

Status	Error	Program
	26.3b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
	3.6b	(.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)))))
	25.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	3.5b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	29.4b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 t z))) 3))
	42.6b	(.f64 (/.f64 x (-.f64 (pow.f64 y 3) (pow.f64 (.f64 z t) 3))) (+.f64 (.f64 y y) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 y (.f64 z t)))))
▶	2.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	3.5b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
	34.5b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))

Compiler

Compiled 2098 to 650 computations (69% saved)

localize12.0ms (0.1%)

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)))
✓	2.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series110.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

72.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
38.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite31.0ms (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:

15.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
7.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify221.0ms (2.5%)

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

prune290.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	182	10	192

Error

2.5b

Counts

192 → 10

Alt Table

Status	Error	Program
	27.0b	(.f64 x (/.f64 1 (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (.f64 z t))))))
	29.4b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 t z))) 3))
	32.1b	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))))
✓	2.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	25.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
▶	3.5b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	26.3b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
	42.6b	(.f64 (/.f64 x (-.f64 (pow.f64 y 3) (pow.f64 (.f64 z t) 3))) (+.f64 (.f64 y y) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 y (.f64 z t)))))
	3.5b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
	34.5b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))

Compiler

Compiled 3617 to 1446 computations (60% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(cbrt.f64 x)
✓	1.4b	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
✓	1.6b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))

series686.0ms (7.7%)

Counts

4 → 120

Calls

4 calls:

456.0ms	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
101.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
73.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
56.0ms	(cbrt.f64 x)

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`
49×	`cbrt-prod_binary64`

Counts

4 → 165

Calls

4 calls:

16.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
9.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
9.0ms	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify400.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
412×	`unswap-sqr_binary64`
344×	`associate-/l*_binary64`
220×	`div-sub_binary64`
183×	`times-frac_binary64`

Counts

285 → 293

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	254	5914
1	620	5095
2	2919	4957
3	4021	4873
4	4838	4873
5	4976	4873

prune411.0ms (4.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	328	1	329
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	329	10	339

Error

2.5b

Counts

339 → 10

Alt Table

Status	Error	Program
	27.0b	(.f64 x (/.f64 1 (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (.f64 z t))))))
	29.4b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 t z))) 3))
	25.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	3.5b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	26.3b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
	42.6b	(.f64 (/.f64 x (-.f64 (pow.f64 y 3) (pow.f64 (.f64 z t) 3))) (+.f64 (.f64 y y) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 y (.f64 z t)))))
✓	2.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
▶	3.5b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
	34.5b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
	3.9b	(/.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)) (/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x)))

Compiler

Compiled 7500 to 1637 computations (78.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t))))
✓	0.4b	(.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t))))
✓	2.7b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
✓	7.5b	(cbrt.f64 (-.f64 y (*.f64 z t)))

series336.0ms (3.8%)

Counts

4 → 156

Calls

4 calls:

118.0ms	(.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t))))
103.0ms	(cbrt.f64 (-.f64 y (*.f64 z t)))
75.0ms	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
40.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t))))

rewrite123.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`cbrt-div_binary64`
61×	`flip--_binary64`
61×	`flip3--_binary64`
60×	`frac-times_binary64`
30×	`associate-*l/_binary64`

Counts

4 → 180

Calls

4 calls:

26.0ms	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
22.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t))))
15.0ms	(.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t))))
3.0ms	(cbrt.f64 (-.f64 y (*.f64 z t)))

simplify300.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

514×	`associate-/r*_binary64`
496×	`times-frac_binary64`
296×	`associate-/l*_binary64`
222×	`fma-def_binary64`
184×	`*-commutative_binary64`

Counts

336 → 398

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	571	11010
1	1611	10312
2	4973	10312

prune926.0ms (10.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	558	0	558
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	558	10	568

Error

2.5b

Counts

568 → 10

Alt Table

Status	Error	Program
	27.0b	(.f64 x (/.f64 1 (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (.f64 z t))))))
	29.4b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 t z))) 3))
	25.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	3.5b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	26.3b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
	42.6b	(.f64 (/.f64 x (-.f64 (pow.f64 y 3) (pow.f64 (.f64 z t) 3))) (+.f64 (.f64 y y) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 y (.f64 z t)))))
✓	2.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	3.5b	(/.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
	34.5b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
	3.9b	(/.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)) (/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x)))

Compiler

Compiled 23736 to 8005 computations (66.3% saved)

regimes1.8s (20.1%)

Accuracy

Total 0.0b remaining (1.5%)

Threshold costs 0.0b (1.5%)

Counts

141 → 1

Compiler

Compiled 18868 to 10863 computations (42.4% 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	15	10
1	23	10
2	32	10
3	38	10
4	42	10
5	43	10
6	40	10

end18.0ms (0.2%)

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

sample1.3s (14.2%)

Algorithm

1×

intervals

Results

499.0ms	8000×	body	128	valid
19.0ms	315×	body	128	invalid

Compiler

Compiled 244 to 132 computations (45.9% 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 (15.1%)

sample46.0ms (0.5%)

simplify29.0ms (0.3%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series81.0ms (0.9%)

rewrite16.0ms (0.2%)

simplify174.0ms (2%)

prune180.0ms (2%)

localize12.0ms (0.1%)

series110.0ms (1.2%)

rewrite31.0ms (0.3%)

simplify221.0ms (2.5%)

prune290.0ms (3.3%)

localize19.0ms (0.2%)

series686.0ms (7.7%)

rewrite63.0ms (0.7%)

simplify400.0ms (4.5%)

prune411.0ms (4.6%)

localize17.0ms (0.2%)

series336.0ms (3.8%)

rewrite123.0ms (1.4%)

simplify300.0ms (3.4%)

prune926.0ms (10.4%)

regimes1.8s (20.1%)

simplify5.0ms (0.1%)

end18.0ms (0.2%)

sample1.3s (14.2%)

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