Details

analyze512.0ms (12.1%)

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)

sample157.0ms (3.7%)

Algorithm

1×

intervals

Symmetry

(sort z t)

Results

8.0ms	256×	body	128	valid
0.0ms	13×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify12.0ms (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

2.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.9b	(/.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))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))

series54.0ms (1.3%)

Counts

2 → 84

Calls

2 calls:

43.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
11.0ms	(-.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))

simplify80.0ms (1.9%)

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

prune84.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	8	111

Error

2.9b

Counts

111 → 8

Alt Table

Status	Error	Program
▶	3.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	28.5b	(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)))))
	3.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
	3.4b	(/.f64 x (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 z t))))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.4b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	3.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))

Compiler

Compiled 1995 to 603 computations (69.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.1b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series60.0ms (1.4%)

Counts

2 → 84

Calls

2 calls:

37.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
23.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite14.0ms (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:

7.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
3.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify101.0ms (2.4%)

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

prune143.0ms (3.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	182	9	191

Error

2.9b

Counts

191 → 9

Alt Table

Status	Error	Program
✓	3.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	28.5b	(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)))))
	3.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
	3.4b	(/.f64 x (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 z t))))
	35.3b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (-.f64 y (*.f64 z t)))))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.4b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
▶	3.2b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))

Compiler

Compiled 3510 to 1389 computations (60.4% 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))
✓	2.9b	(/.f64 (-.f64 y (*.f64 z t)) x)

series62.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

44.0ms	(/.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:

6.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
4.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify120.0ms (2.8%)

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

prune168.0ms (4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	227	8	235

Error

2.9b

Counts

235 → 8

Alt Table

Status	Error	Program
▶	3.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
	4.2b	(/.f64 1 (-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x)))
✓	3.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	28.5b	(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)))))
	35.3b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (-.f64 y (*.f64 z t)))))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.4b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))

Compiler

Compiled 4387 to 1394 computations (68.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (.f64 (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))))
✓	0.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
✓	8.4b	(cbrt.f64 (-.f64 y (*.f64 z t)))

series246.0ms (5.8%)

Counts

4 → 156

Calls

4 calls:

85.0ms	(/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
71.0ms	(.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t))))
49.0ms	(cbrt.f64 (-.f64 y (*.f64 z t)))
39.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))

rewrite61.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-exp-log_binary64`
59×	`add-sqr-sqrt_binary64`
40×	`cbrt-div_binary64`
36×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`

Counts

4 → 192

Calls

4 calls:

22.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
10.0ms	(/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t)))))
7.0ms	(.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (*.f64 z t))))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 z t)))

simplify307.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

811×	`times-frac_binary64`
359×	`fma-def_binary64`
249×	`*-commutative_binary64`
121×	`cancel-sign-sub-inv_binary64`
118×	`fma-neg_binary64`

Counts

348 → 478

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	717	13646
1	2218	11896
2	4782	11696
3	4999	11676
4	4952	11676

prune533.0ms (12.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	643	1	644
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	644	8	652

Error

2.9b

Counts

652 → 8

Alt Table

Status	Error	Program
✓	3.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
	4.2b	(/.f64 1 (-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x)))
	35.3b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (-.f64 y (*.f64 z t)))))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.4b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	3.1b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	3.7b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z)))))) (/.f64 x (cbrt.f64 (cbrt.f64 (-.f64 y (.f64 z t))))))

Compiler

Compiled 27546 to 10129 computations (63.2% saved)

regimes784.0ms (18.5%)

Accuracy

Total 0.1b remaining (2.4%)

Threshold costs 0.1b (2.4%)

Counts

103 → 1

Compiler

Compiled 15123 to 8650 computations (42.8% saved)

simplify6.0ms (0.2%)

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

end6.0ms (0.1%)

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

sample663.0ms (15.7%)

Algorithm

1×

intervals

Results

280.0ms	8000×	body	128	valid
13.0ms	363×	body	128	invalid

Compiler

Compiled 194 to 105 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

analyze512.0ms (12.1%)

sample157.0ms (3.7%)

simplify12.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series54.0ms (1.3%)

rewrite8.0ms (0.2%)

simplify80.0ms (1.9%)

prune84.0ms (2%)

localize6.0ms (0.1%)

series60.0ms (1.4%)

rewrite14.0ms (0.3%)

simplify101.0ms (2.4%)

prune143.0ms (3.4%)

localize6.0ms (0.2%)

series62.0ms (1.5%)

rewrite22.0ms (0.5%)

simplify120.0ms (2.8%)

prune168.0ms (4%)

localize10.0ms (0.2%)

series246.0ms (5.8%)

rewrite61.0ms (1.4%)

simplify307.0ms (7.2%)

prune533.0ms (12.6%)

regimes784.0ms (18.5%)

simplify6.0ms (0.2%)

end6.0ms (0.1%)

sample663.0ms (15.7%)

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