Details

analyze576.0ms (14.8%)

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
25%	74.9%	0.2%	5
25%	74.9%	0.2%	6
31.2%	68.6%	0.2%	7
40.5%	59.3%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
54.6%	45.2%	0.2%	11
67.1%	32.7%	0.2%	12
73.3%	26.5%	0.2%	13
73.3%	26.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample952.0ms (24.5%)

Infinites

0% of outputs are infinite.

Results

864.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify55.0ms (1.4%)

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

2.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.5b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	12.9b	(-.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)))))
✓	4.4b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	6.7b	(/.f64 (.f64 y t) (.f64 2 z))

series96.0ms (2.5%)

Counts

4 → 156

Calls

4 calls:

42.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
28.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
13.0ms	(/.f64 (.f64 y t) (.f64 2 z))
12.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

rewrite48.0ms (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:

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

simplify242.0ms (6.2%)

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

prune242.0ms (6.2%)

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
	3.6b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
	3.6b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
▶	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	23.9b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 11556 to 5784 computations (49.9% 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)))
✓	4.0b	(*.f64 (/.f64 y 2) (/.f64 t z))
✓	4.4b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

series107.0ms (2.8%)

Counts

4 → 156

Calls

4 calls:

45.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
28.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
20.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))
14.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))

rewrite43.0ms (1.1%)

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:

9.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
8.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
6.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
3.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))

simplify203.0ms (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 → 278

Iterations

Useful iterations: 3 (0.0ms)

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

prune218.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	278	4	282

Error

Counts

282 → 4

Alt Table

Status	Error	Program
	3.6b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
▶	3.6b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
✓	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	23.9b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 9558 to 4878 computations (49% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	1.0b	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
✓	4.1b	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)
	6.7b	(/.f64 (.f64 y t) (.f64 2 z))

series48.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

31.0ms	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
16.0ms	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)

rewrite30.0ms (0.8%)

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:

7.0ms	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
6.0ms	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)

simplify147.0ms (3.8%)

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

prune225.0ms (5.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	304	1	305
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	306	3	309

Error

Counts

309 → 3

Alt Table

Status	Error	Program
✓	3.6b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
	23.9b	(fma.f64 2 (/.f64 z t) x)
▶	2.2b	(-.f64 x (.f64 (/.f64 1 (fma.f64 -1/2 (.f64 (/.f64 y z) t) z)) y))

Compiler

Compiled 8467 to 4507 computations (46.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 -1/2 (*.f64 (/.f64 y z) t) z)
✓	0.7b	(/.f64 1 (fma.f64 -1/2 (*.f64 (/.f64 y z) t) z))
✓	3.2b	(*.f64 (/.f64 y z) t)
✓	3.8b	(.f64 (/.f64 1 (fma.f64 -1/2 (.f64 (/.f64 y z) t) z)) y)

series85.0ms (2.2%)

Counts

4 → 144

Calls

4 calls:

32.0ms	(/.f64 1 (fma.f64 -1/2 (*.f64 (/.f64 y z) t) z))
28.0ms	(.f64 (/.f64 1 (fma.f64 -1/2 (.f64 (/.f64 y z) t) z)) y)
13.0ms	(fma.f64 -1/2 (*.f64 (/.f64 y z) t) z)
12.0ms	(*.f64 (/.f64 y z) t)

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
29×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`

Counts

4 → 114

Calls

4 calls:

5.0ms	(/.f64 1 (fma.f64 -1/2 (*.f64 (/.f64 y z) t) z))
5.0ms	(.f64 (/.f64 1 (fma.f64 -1/2 (.f64 (/.f64 y z) t) z)) y)
4.0ms	(*.f64 (/.f64 y z) t)
0.0ms	(fma.f64 -1/2 (*.f64 (/.f64 y z) t) z)

simplify134.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

774×	`associate-/r*_binary64`
574×	`associate-*l/_binary64`
329×	`fma-def_binary64`
183×	`associate-/r/_binary64`
140×	`fma-neg_binary64`

Counts

258 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	5076
1	544	4778
2	1879	4738
3	4982	4738
4	5019	4738

prune142.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	205	3	208

Error

Counts

208 → 3

Alt Table

Status	Error	Program
✓	3.6b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
	23.9b	(fma.f64 2 (/.f64 z t) x)
✓	2.2b	(-.f64 x (.f64 (/.f64 1 (fma.f64 -1/2 (.f64 (/.f64 y z) t) z)) y))

Compiler

Compiled 4802 to 2437 computations (49.3% saved)

regimes161.0ms (4.1%)

Accuracy

Total 0.1b remaining (72%)

Threshold costs 0.1b (72%)

Counts

26 → 1

Compiler

Compiled 2728 to 1864 computations (31.7% saved)

simplify2.0ms (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

end62.0ms (1.6%)

Compiler: Compiled 79 to 54 computations (31.6% saved)

Details

analyze576.0ms (14.8%)

sample952.0ms (24.5%)

simplify55.0ms (1.4%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series96.0ms (2.5%)

rewrite48.0ms (1.2%)

simplify242.0ms (6.2%)

prune242.0ms (6.2%)

localize9.0ms (0.2%)

series107.0ms (2.8%)

rewrite43.0ms (1.1%)

simplify203.0ms (5.2%)

prune218.0ms (5.6%)

localize11.0ms (0.3%)

series48.0ms (1.2%)

rewrite30.0ms (0.8%)

simplify147.0ms (3.8%)

prune225.0ms (5.8%)

localize10.0ms (0.2%)

series85.0ms (2.2%)

rewrite21.0ms (0.5%)

simplify134.0ms (3.5%)

prune142.0ms (3.7%)

regimes161.0ms (4.1%)

simplify2.0ms (0.1%)

end62.0ms (1.6%)

Profiling