Details

analyze1.1s (22.3%)

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
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)

sample1.2s (24.1%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify56.0ms (1.1%)

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

2.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.1b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	12.1b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize9.0ms (0.2%)

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)))))
✓	3.8b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	5.6b	(/.f64 (.f64 y t) (.f64 2 z))

series105.0ms (2.1%)

Counts

4 → 156

Calls

4 calls:

47.0ms	(-.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))))
15.0ms	(/.f64 (.f64 y t) (.f64 2 z))
12.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

rewrite52.0ms (1%)

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:

11.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
6.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
5.0ms	(/.f64 (.f64 y t) (.f64 2 z))
5.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

simplify254.0ms (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 → 309

Iterations

Useful iterations: 2 (0.0ms)

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

prune267.0ms (5.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	305	4	309
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	307	4	311

Error

Counts

311 → 4

Alt Table

Status	Error	Program
	28.8b	(fma.f64 2 (/.f64 z t) x)
▶	1.2b	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
	3.1b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
	3.2b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))

Compiler

Compiled 11558 to 5786 computations (49.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
✓	0.0b	(+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))
✓	3.8b	(/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))))
✓	5.7b	(*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))

series111.0ms (2.2%)

Counts

4 → 156

Calls

4 calls:

49.0ms	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
33.0ms	(/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))))
17.0ms	(*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))
12.0ms	(+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))

rewrite53.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-sqr-sqrt_binary64`
81×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
74×	`times-frac_binary64`
45×	`prod-diff_binary64`

Counts

4 → 191

Calls

4 calls:

18.0ms	(*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))
10.0ms	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
4.0ms	(/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z))))
3.0ms	(+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))

simplify270.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

297×	`fma-neg_binary64`
246×	`associate-*r/_binary64`
229×	`*-commutative_binary64`
217×	`associate-*l/_binary64`
183×	`associate-/l*_binary64`

Counts

347 → 323

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	424	10613
1	1194	8050
2	3633	7194
3	4655	7194
4	5000	7194
5	4817	7194

prune303.0ms (5.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	323	4	327

Error

Counts

327 → 4

Alt Table

Status	Error	Program
	28.8b	(fma.f64 2 (/.f64 z t) x)
✓	1.2b	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
▶	3.1b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
	3.2b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))

Compiler

Compiled 11148 to 6018 computations (46% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	0.3b	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	3.6b	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
	5.6b	(/.f64 (.f64 y t) (.f64 2 z))

series59.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

31.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
28.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

2 → 89

Calls

2 calls:

10.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
5.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

simplify96.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

768×	`associate-/r*_binary64`
520×	`associate-*l/_binary64`
347×	`fma-def_binary64`
216×	`associate-/r/_binary64`
174×	`associate-/l/_binary64`

Counts

161 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	4402
1	458	4169
2	1716	4122
3	5191	4122

prune199.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	248	4	252

Error

Counts

252 → 4

Alt Table

Status	Error	Program
	28.8b	(fma.f64 2 (/.f64 z t) x)
✓	1.2b	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
✓	3.1b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
▶	3.2b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))

Compiler

Compiled 6790 to 3808 computations (43.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	0.9b	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
✓	3.6b	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)
	5.6b	(/.f64 (.f64 y t) (.f64 2 z))

series48.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

29.0ms	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
18.0ms	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`times-frac_binary64`
100×	`*-un-lft-identity_binary64`
100×	`add-sqr-sqrt_binary64`
68×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

2 → 142

Calls

2 calls:

8.0ms	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
7.0ms	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)

simplify156.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

891×	`fma-def_binary64`
712×	`associate-/l*_binary64`
579×	`associate-/r*_binary64`
379×	`associate-/r/_binary64`
352×	`associate-/l/_binary64`

Counts

214 → 212

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	5873
1	458	5514
2	1569	5390
3	4891	5054
4	5505	5054

prune252.0ms (5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	305	4	309

Error

Counts

309 → 4

Alt Table

Status	Error	Program
	28.8b	(fma.f64 2 (/.f64 z t) x)
✓	1.2b	(-.f64 x (/.f64 y (+.f64 z (*.f64 (neg.f64 (/.f64 y 2)) (/.f64 t z)))))
✓	3.1b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
✓	3.2b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))

Compiler

Compiled 8458 to 4501 computations (46.8% saved)

regimes284.0ms (5.6%)

Accuracy

Total 0.1b remaining (92.6%)

Threshold costs 0.1b (92.6%)

Counts

45 → 1

Compiler

Compiled 5248 to 3484 computations (33.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	16	17
2	22	17
3	24	17
4	25	17
5	23	17

end66.0ms (1.3%)

Compiler: Compiled 98 to 67 computations (31.6% saved)

Details

analyze1.1s (22.3%)

sample1.2s (24.1%)

simplify56.0ms (1.1%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series105.0ms (2.1%)

rewrite52.0ms (1%)

simplify254.0ms (5%)

prune267.0ms (5.2%)

localize10.0ms (0.2%)

series111.0ms (2.2%)

rewrite53.0ms (1%)

simplify270.0ms (5.3%)

prune303.0ms (5.9%)

localize10.0ms (0.2%)

series59.0ms (1.2%)

rewrite22.0ms (0.4%)

simplify96.0ms (1.9%)

prune199.0ms (3.9%)

localize10.0ms (0.2%)

series48.0ms (0.9%)

rewrite31.0ms (0.6%)

simplify156.0ms (3.1%)

prune252.0ms (5%)

regimes284.0ms (5.6%)

simplify3.0ms (0.1%)

end66.0ms (1.3%)

Profiling