Details

analyze1.3s (20.2%)

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
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
22.2%	77.6%	0.2%	11
40.4%	59.5%	0.2%	12
47.4%	52.4%	0.2%	13
55.3%	44.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.1s (17.9%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
504×	`associate-*l/_binary64`
466×	`div-sub_binary64`
450×	`cancel-sign-sub-inv_binary64`
403×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	30	25
2	70	25
3	177	22
4	486	19
5	1087	19
6	2534	19
7	4434	19
8	5156	19

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

2.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	10.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	3.2b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	4.5b	(/.f64 (.f64 y t) (.f64 2 z))
✓	5.7b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

series92.0ms (1.5%)

Counts

4 → 156

Calls

4 calls:

38.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
23.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
20.0ms	(/.f64 (.f64 y t) (.f64 2 z))
10.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`add-sqr-sqrt_binary64`
118×	`*-un-lft-identity_binary64`
82×	`add-cube-cbrt_binary64`
81×	`times-frac_binary64`
78×	`prod-diff_binary64`

Counts

4 → 203

Calls

4 calls:

12.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
7.0ms	(/.f64 (.f64 y t) (.f64 2 z))
5.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
4.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

simplify1.9s (30.8%)

Algorithm

1×	egg-herbie

Rules

335×	`fma-neg_binary64`
273×	`exp-prod_binary64`
232×	`times-frac_binary64`
230×	`associate-/l*_binary64`
215×	`associate-*r/_binary64`

Counts

359 → 312

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	11732
1	1154	9150
2	3814	7711
3	4584	7711
4	4860	7711

prune269.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	310	2	312
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	311	3	314

Error

Counts

314 → 3

Alt Table

Status	Error	Program
	10.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	22.1b	(fma.f64 2 (/.f64 z t) x)
▶	2.7b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))

Compiler

Compiled 11561 to 5777 computations (50% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (.f64 (/.f64 y z) t))
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
✓	4.6b	(*.f64 (/.f64 y z) t)
✓	5.7b	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))

series81.0ms (1.3%)

Counts

4 → 156

Calls

4 calls:

35.0ms	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
21.0ms	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
12.0ms	(.f64 1/2 (.f64 (/.f64 y z) t))
12.0ms	(*.f64 (/.f64 y z) t)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
67×	`*-un-lft-identity_binary64`
65×	`add-cube-cbrt_binary64`
56×	`times-frac_binary64`
45×	`prod-diff_binary64`

Counts

4 → 167

Calls

4 calls:

8.0ms	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
5.0ms	(*.f64 (/.f64 y z) t)
5.0ms	(.f64 1/2 (.f64 (/.f64 y z) t))
3.0ms	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))

simplify229.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

290×	`cancel-sign-sub-inv_binary64`
258×	`fma-neg_binary64`
227×	`distribute-neg-frac_binary64`
181×	`associate-r_binary64`
178×	`*-commutative_binary64`

Counts

323 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	383	8954
1	1000	7181
2	3056	6335
3	4628	6325
4	4983	6325
5	4812	6325

prune186.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	237	3	240

Error

Counts

240 → 3

Alt Table

Status	Error	Program
▶	10.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	22.1b	(fma.f64 2 (/.f64 z t) x)
✓	2.7b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))

Compiler

Compiled 8639 to 3895 computations (54.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	1.1b	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))
✓	19.5b	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))

series88.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

49.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
26.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))
12.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`prod-diff_binary64`
25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`

Counts

3 → 97

Calls

3 calls:

9.0ms	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
7.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))
4.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))

simplify170.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

333×	`cancel-sign-sub-inv_binary64`
312×	`fma-neg_binary64`
231×	`associate-l_binary64`
217×	`associate-r_binary64`
196×	`exp-prod_binary64`

Counts

217 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	6068
1	795	5719
2	3182	5532
3	4652	5532
4	4843	5532

prune151.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	191	3	194

Error

Counts

194 → 3

Alt Table

Status	Error	Program
✓	10.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	22.1b	(fma.f64 2 (/.f64 z t) x)
✓	2.7b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))

Compiler

Compiled 7340 to 4026 computations (45.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 z t) x)

series8.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 2 (/.f64 z t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 2 (/.f64 z t) x)

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-*l/_binary64`
542×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
443×	`associate-+l+_binary64`
396×	`fma-def_binary64`

Counts

46 → 14

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	376
1	23	359
2	49	359
3	126	359
4	432	359
5	1628	359
6	4283	359
7	4686	359
8	4929	359
9	4999	359

prune9.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	14	3	17

Error

Counts

17 → 3

Alt Table

Status	Error	Program
✓	10.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	22.1b	(fma.f64 2 (/.f64 z t) x)
✓	2.7b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))

Compiler

Compiled 187 to 100 computations (46.5% saved)

regimes319.0ms (5.1%)

Accuracy

Total 1.5b remaining (99.5%)

Threshold costs 0b (0%)

Counts

56 → 2

Compiler

Compiled 6046 to 4156 computations (31.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 21 to 14 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
19×	`+-commutative_binary64`
19×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	68
1	59	68
2	91	68
3	122	68
4	148	68
5	157	68
6	160	68
7	157	68

end65.0ms (1%)

Compiler: Compiled 148 to 92 computations (37.8% saved)

Details

analyze1.3s (20.2%)

sample1.1s (17.9%)

simplify54.0ms (0.9%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series92.0ms (1.5%)

rewrite50.0ms (0.8%)

simplify1.9s (30.8%)

prune269.0ms (4.3%)

localize9.0ms (0.1%)

series81.0ms (1.3%)

rewrite36.0ms (0.6%)

simplify229.0ms (3.6%)

prune186.0ms (3%)

localize11.0ms (0.2%)

series88.0ms (1.4%)

rewrite28.0ms (0.4%)

simplify170.0ms (2.7%)

prune151.0ms (2.4%)

localize5.0ms (0.1%)

series8.0ms (0.1%)

rewrite1.0ms (0%)

simplify75.0ms (1.2%)

prune9.0ms (0.1%)

regimes319.0ms (5.1%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end65.0ms (1%)

Profiling