Details

analyze734.0ms (7.3%)

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
12.5%	87.3%	0.2%	7
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
43.7%	56.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.1s (10.5%)

Symmetry

(sort z t)

Results

944.0ms	8256×	body	128	valid
47.0ms	376×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify122.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1226×	`div-sub_binary64`
778×	`fma-def_binary64`
701×	`unsub-neg_binary64`
456×	`sub-neg_binary64`
437×	`fma-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	16
2	50	16
3	121	16
4	299	16
5	674	16
6	1361	16
7	2742	16
8	3706	16
9	3871	16
10	4083	16
11	4304	16
12	4387	16
13	5424	16

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

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	7.6b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series132.0ms (1.3%)

Counts

2 → 84

Calls

2 calls:

123.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
8.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

8.0ms	(*.f64 (-.f64 y z) (-.f64 y t))
7.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
589×	`associate-/l*_binary64`
505×	`associate-/r*_binary64`
195×	`fma-def_binary64`
134×	`*-commutative_binary64`

Counts

173 → 187

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	5989
1	1376	5678
2	5010	5678

prune183.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	181	6	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	6	188

Error

0.0b

Counts

188 → 6

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y t) (-.f64 y z))))
	1.1b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	1.0b	(-.f64 1 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 (-.f64 y z) (-.f64 y t)) (cbrt.f64 x))))
	37.2b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 (.f64 y y) (.f64 t t)))) (*.f64 (+.f64 y z) (+.f64 y t))))
	0.9b	(-.f64 1 (/.f64 x (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (-.f64 y z)) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z)))))
	1.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))

Compiler

Compiled 6501 to 2681 computations (58.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y t) (-.f64 y z))
✓	7.6b	(/.f64 x (*.f64 (-.f64 y t) (-.f64 y z)))

series131.0ms (1.3%)

Counts

2 → 80

Calls

2 calls:

122.0ms	(/.f64 x (*.f64 (-.f64 y t) (-.f64 y z)))
8.0ms	(*.f64 (-.f64 y t) (-.f64 y z))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

9.0ms	(/.f64 x (*.f64 (-.f64 y t) (-.f64 y z)))
7.0ms	(*.f64 (-.f64 y t) (-.f64 y z))

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Rules

689×	`times-frac_binary64`
554×	`associate-/l*_binary64`
496×	`associate-/r*_binary64`
200×	`fma-def_binary64`
133×	`*-commutative_binary64`

Counts

169 → 186

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	442	5937
1	1377	5626
2	5058	5626

prune193.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	186	6	192

Error

0.0b

Counts

192 → 6

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y t) (-.f64 y z))))
	1.1b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	1.0b	(-.f64 1 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 (-.f64 y z) (-.f64 y t)) (cbrt.f64 x))))
	37.2b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 (.f64 y y) (.f64 t t)))) (*.f64 (+.f64 y z) (+.f64 y t))))
▶	0.9b	(-.f64 1 (/.f64 x (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (-.f64 y z)) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z)))))
	1.6b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))

Compiler

Compiled 6475 to 2669 computations (58.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1)))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	7.6b	(/.f64 x (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (-.f64 y z)) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z))))

series1.5s (14.5%)

Counts

4 → 96

Calls

4 calls:

1.2s	(/.f64 x (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (-.f64 y z)) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z))))
158.0ms	(fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1)))
35.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
29.0ms	(cbrt.f64 y)

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
19×	`cbrt-prod_binary64`
12×	`times-frac_binary64`

Counts

4 → 104

Calls

4 calls:

8.0ms	(/.f64 x (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (-.f64 y z)) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z))))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
0.0ms	(fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1)))

simplify113.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

845×	`associate-/l*_binary64`
682×	`associate-/r*_binary64`
306×	`fma-def_binary64`
135×	`*-commutative_binary64`
126×	`+-commutative_binary64`

Counts

200 → 237

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	551	6676
1	1887	6055
2	5648	6055

prune349.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	269	2	271
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	272	5	277

Error

Counts

277 → 5

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y t) (-.f64 y z))))
	1.1b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	37.2b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 (.f64 y y) (.f64 t t)))) (*.f64 (+.f64 y z) (+.f64 y t))))
	1.7b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (+.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (fma.f64 (neg.f64 t) 1 (*.f64 t 1)))))
▶	1.0b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (-.f64 y z)) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z))))))

Compiler

Compiled 13827 to 6389 computations (53.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 x)
	0.6b	(cbrt.f64 y)
✓	3.6b	(/.f64 (cbrt.f64 x) (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (-.f64 y z)) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z))))
✓	4.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (-.f64 y z)) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z)))))

series2.8s (28.1%)

Counts

3 → 108

Calls

3 calls:

1.4s

(/.f64 (cbrt.f64 x) (+.f64 (*.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 t 1))) (-.f64 y z)) (*.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z))))

1.4s

(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) (+.f64 (*.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 t 1))) (-.f64 y z)) (*.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z)))))

54.0ms

(cbrt.f64 x)

rewrite60.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
38×	`add-exp-log_binary64`

Counts

3 → 147

Calls

3 calls:

24.0ms

(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) (+.f64 (*.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 t 1))) (-.f64 y z)) (*.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z)))))

7.0ms

(/.f64 (cbrt.f64 x) (+.f64 (*.f64 (fma.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (*.f64 t 1))) (-.f64 y z)) (*.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z))))

1.0ms

(cbrt.f64 x)

simplify226.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-def_binary64`
318×	`*-commutative_binary64`
238×	`+-commutative_binary64`
211×	`sub-neg_binary64`
155×	`cancel-sign-sub-inv_binary64`

Counts

255 → 392

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	975	16492
1	3574	13361
2	4965	13361

prune1.2s (12%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	477	0	477
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	477	5	482

Error

Counts

482 → 5

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y t) (-.f64 y z))))
	1.1b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	37.2b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 (.f64 y y) (.f64 t t)))) (*.f64 (+.f64 y z) (+.f64 y t))))
	1.7b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (+.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (fma.f64 (neg.f64 t) 1 (*.f64 t 1)))))
✓	1.0b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 x) (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (neg.f64 (.f64 t 1))) (-.f64 y z)) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) (-.f64 y z))))))

Compiler

Compiled 30511 to 13709 computations (55.1% saved)

regimes854.0ms (8.5%)

Accuracy

Total 0.6b remaining (97.7%)

Threshold costs 0.6b (97.7%)

Counts

106 → 1

Compiler

Compiled 20471 to 12300 computations (39.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	26	34
2	38	34
3	49	34
4	56	34
5	59	34
6	60	34
7	59	34

end98.0ms (1%)

Remove: (sort z t)
Compiler: Compiled 244 to 151 computations (38.1% saved)

Details

analyze734.0ms (7.3%)

sample1.1s (10.5%)

simplify122.0ms (1.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series132.0ms (1.3%)

rewrite20.0ms (0.2%)

simplify101.0ms (1%)

prune183.0ms (1.8%)

localize7.0ms (0.1%)

series131.0ms (1.3%)

rewrite23.0ms (0.2%)

simplify99.0ms (1%)

prune193.0ms (1.9%)

localize18.0ms (0.2%)

series1.5s (14.5%)

rewrite20.0ms (0.2%)

simplify113.0ms (1.1%)

prune349.0ms (3.5%)

localize21.0ms (0.2%)

series2.8s (28.1%)

rewrite60.0ms (0.6%)

simplify226.0ms (2.2%)

prune1.2s (12%)

regimes854.0ms (8.5%)

simplify3.0ms (0%)

end98.0ms (1%)

Profiling