Details

analyze1.0s (24%)

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)

sample1.3s (29.4%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify81.0ms (1.9%)

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

1.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	9.6b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	2.5b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	4.8b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	5.4b	(/.f64 (.f64 y t) (.f64 2 z))

series105.0ms (2.4%)

Counts

4 → 156

Calls

4 calls:

46.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
31.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
16.0ms	(/.f64 (.f64 y t) (.f64 2 z))
12.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

rewrite52.0ms (1.2%)

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:

13.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
5.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
5.0ms	(/.f64 (.f64 y t) (.f64 2 z))
5.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

simplify238.0ms (5.5%)

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 → 310

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	10640
1	1154	8682
2	3814	7711
3	4584	7711
4	4860	7711

prune241.0ms (5.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	307	3	310
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	309	3	312

Error

Counts

312 → 3

Alt Table

Status	Error	Program
	28.1b	(-.f64 x (.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (*.f64 y t) z) -1/2)))))
	27.0b	(fma.f64 2 (/.f64 z t) x)
▶	1.2b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 11535 to 5763 computations (50% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	0.0b	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))
✓	4.8b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
✓	5.8b	(*.f64 (/.f64 y 2) (/.f64 t z))

series113.0ms (2.6%)

Counts

4 → 156

Calls

4 calls:

48.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
31.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
21.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
13.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
72×	`add-cube-cbrt_binary64`
68×	`times-frac_binary64`
48×	`prod-diff_binary64`

Counts

4 → 182

Calls

4 calls:

8.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
7.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
3.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
3.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))

simplify223.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

285×	`fma-neg_binary64`
275×	`distribute-neg-frac_binary64`
251×	`cancel-sign-sub-inv_binary64`
247×	`associate-*r/_binary64`
230×	`associate-*l/_binary64`

Counts

338 → 277

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	416	9325
1	1131	7563
2	3407	6952
3	4955	6942
4	4882	6942

prune197.0ms (4.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	277	3	280

Error

Counts

280 → 3

Alt Table

Status	Error	Program
	28.1b	(-.f64 x (.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (*.f64 y t) z) -1/2)))))
▶	27.0b	(fma.f64 2 (/.f64 z t) x)
✓	1.2b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 9511 to 4846 computations (49% saved)

localize5.0ms (0.1%)

prune2.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
▶	28.1b	(-.f64 x (.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (*.f64 y t) z) -1/2)))))
✓	27.0b	(fma.f64 2 (/.f64 z t) x)
✓	1.2b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 z (.f64 (/.f64 (.f64 y t) z) -1/2))
✓	1.4b	(.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (*.f64 y t) z) -1/2))))
✓	1.8b	(/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (.f64 y t) z) -1/2)))
✓	5.4b	(/.f64 (*.f64 y t) z)

series162.0ms (3.8%)

Counts

4 → 92

Calls

4 calls:

71.0ms	(/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (.f64 y t) z) -1/2)))
43.0ms	(.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (*.f64 y t) z) -1/2))))
35.0ms	(/.f64 (*.f64 y t) z)
13.0ms	(+.f64 z (.f64 (/.f64 (.f64 y t) z) -1/2))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
29×	`sqrt-prod_binary64`

Counts

4 → 134

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (*.f64 y t) z) -1/2))))
6.0ms	(/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (.f64 y t) z) -1/2)))
3.0ms	(/.f64 (*.f64 y t) z)
3.0ms	(+.f64 z (.f64 (/.f64 (.f64 y t) z) -1/2))

simplify121.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

588×	`associate-/l/_binary64`
573×	`fma-def_binary64`
171×	`associate-/l*_binary64`
164×	`associate-r_binary64`
163×	`associate-l_binary64`

Counts

226 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	5765
1	712	5210
2	2629	5128
3	5036	5128

prune142.0ms (3.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

240 → 3

Alt Table

Status	Error	Program
✓	28.1b	(-.f64 x (.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (+.f64 z (.f64 (/.f64 (*.f64 y t) z) -1/2)))))
✓	27.0b	(fma.f64 2 (/.f64 z t) x)
✓	1.2b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 6623 to 2803 computations (57.7% saved)

regimes170.0ms (3.9%)

Accuracy

Total 0.9b remaining (99.1%)

Threshold costs 0.9b (99.1%)

Counts

24 → 1

Compiler

Compiled 2884 to 1876 computations (35% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	20	19
2	36	19
3	48	19
4	57	19
5	61	19
6	62	19
7	62	19

end53.0ms (1.2%)

Compiler: Compiled 82 to 53 computations (35.4% saved)

Details

analyze1.0s (24%)

sample1.3s (29.4%)

simplify81.0ms (1.9%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series105.0ms (2.4%)

rewrite52.0ms (1.2%)

simplify238.0ms (5.5%)

prune241.0ms (5.6%)

localize9.0ms (0.2%)

series113.0ms (2.6%)

rewrite42.0ms (1%)

simplify223.0ms (5.2%)

prune197.0ms (4.6%)

localize5.0ms (0.1%)

prune2.0ms (0%)

localize10.0ms (0.2%)

series162.0ms (3.8%)

rewrite33.0ms (0.8%)

simplify121.0ms (2.8%)

prune142.0ms (3.3%)

regimes170.0ms (3.9%)

simplify3.0ms (0.1%)

end53.0ms (1.2%)

Profiling