Details

analyze1.6s (25.7%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0.4%	99.4%	0.2%	10
5.6%	94.2%	0.2%	11
7.1%	92.7%	0.2%	12
8.8%	91%	0.2%	13
15.6%	84.2%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample76.0ms (1.2%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 42 to 30 computations (28.6% saved)

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
683×	`sub-neg_binary64`
438×	`neg-mul-1_binary64`
412×	`neg-sub0_binary64`
378×	`distribute-rgt-out--_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	28	19
2	66	19
3	158	17
4	344	17
5	846	17
6	2066	17
7	3773	17
8	4182	17
9	4701	17
10	4906	17
11	4923	17

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

1.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.7b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	1.8b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 100 to 63 computations (37% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 (-.f64 t z) 1))
✓	1.7b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series95.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

67.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
28.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
8×	`distribute-lft-out_binary64`

Counts

2 → 49

Calls

2 calls:

9.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
1.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

simplify138.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

379×	`times-frac_binary64`
371×	`sub-neg_binary64`
318×	`associate-+r+_binary64`
277×	`+-commutative_binary64`
256×	`associate-/l*_binary64`

Counts

145 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	349	4823
1	1015	4738
2	4256	4723
3	4982	4723
4	5014	4723

prune153.0ms (2.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	145	3	148

Error

0.0b

Counts

148 → 3

Alt Table

Status	Error	Program
▶	1.8b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	36.3b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	10.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 4565 to 2214 computations (51.5% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	6.9b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series68.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

56.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
12.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite46.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

236×	`*-un-lft-identity_binary64`
200×	`times-frac_binary64`
126×	`add-sqr-sqrt_binary64`
86×	`add-cube-cbrt_binary64`
44×	`distribute-lft-out_binary64`

Counts

2 → 179

Calls

2 calls:

14.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
7.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify196.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

397×	`times-frac_binary64`
302×	`associate-/l*_binary64`
300×	`associate-/r/_binary64`
273×	`fma-neg_binary64`
262×	`associate-+r+_binary64`

Counts

263 → 270

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	439	8373
1	1313	7839
2	4937	7839
3	5192	7839

prune266.0ms (4.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	269	4	273

Error

Counts

273 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 x (*.f64 a (/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z))))
	2.6b	(-.f64 x (/.f64 (-.f64 y z) (-.f64 (+.f64 (/.f64 t a) (/.f64 1 a)) (/.f64 z a))))
	10.6b	(-.f64 x (.f64 (/.f64 1 (-.f64 (+.f64 1 t) z)) (.f64 a (-.f64 y z))))
	10.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 8368 to 3835 computations (54.2% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z))
✓	1.5b	(*.f64 a (/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z)))

series93.0ms (1.5%)

Counts

2 → 84

Calls

2 calls:

56.0ms	(*.f64 a (/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z)))
37.0ms	(/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`*-un-lft-identity_binary64`
81×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
36×	`associate-r_binary64`
35×	`distribute-lft-out--_binary64`

Counts

2 → 117

Calls

2 calls:

17.0ms	(*.f64 a (/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z)))
9.0ms	(/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z))

simplify157.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

526×	`times-frac_binary64`
469×	`associate-/l*_binary64`
321×	`fma-neg_binary64`
283×	`associate-/r*_binary64`
209×	`associate--l+_binary64`

Counts

201 → 186

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	513	7081
1	1548	6919
2	4960	6919
3	5259	6919

prune178.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	186	4	190

Error

Counts

190 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 x (.f64 a (.f64 (-.f64 y z) (/.f64 1 (-.f64 (+.f64 1 t) z)))))
✓	0.1b	(-.f64 x (*.f64 a (/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z))))
	2.6b	(-.f64 x (/.f64 (-.f64 y z) (-.f64 (+.f64 (/.f64 t a) (/.f64 1 a)) (/.f64 z a))))
	10.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 7116 to 3655 computations (48.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 (+.f64 1 t) z))
✓	0.2b	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 (+.f64 1 t) z)))
✓	1.5b	(.f64 a (.f64 (-.f64 y z) (/.f64 1 (-.f64 (+.f64 1 t) z))))

series117.0ms (1.9%)

Counts

3 → 108

Calls

3 calls:

67.0ms	(.f64 a (.f64 (-.f64 y z) (/.f64 1 (-.f64 (+.f64 1 t) z))))
34.0ms	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 (+.f64 1 t) z)))
15.0ms	(/.f64 1 (-.f64 (+.f64 1 t) z))

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
31×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`

Counts

3 → 132

Calls

3 calls:

17.0ms	(*.f64 (-.f64 y z) (/.f64 1 (-.f64 (+.f64 1 t) z)))
13.0ms	(.f64 a (.f64 (-.f64 y z) (/.f64 1 (-.f64 (+.f64 1 t) z))))
6.0ms	(/.f64 1 (-.f64 (+.f64 1 t) z))

simplify496.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

519×	`times-frac_binary64`
368×	`associate-/l*_binary64`
340×	`fma-neg_binary64`
295×	`associate-/r*_binary64`
237×	`associate--l+_binary64`

Counts

240 → 262

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	575	7923
1	1704	7514
2	4959	7514
3	5270	7514

prune242.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	262	4	266

Error

Counts

266 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 x (.f64 a (.f64 (-.f64 y z) (/.f64 1 (-.f64 (+.f64 1 t) z)))))
✓	0.1b	(-.f64 x (*.f64 a (/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z))))
	2.6b	(-.f64 x (/.f64 (-.f64 y z) (-.f64 (+.f64 (/.f64 t a) (/.f64 1 a)) (/.f64 z a))))
	10.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 9140 to 5065 computations (44.6% saved)

regimes1.1s (18.3%)

Accuracy

Total 0.2b remaining (93.3%)

Threshold costs 0.2b (93.3%)

Counts

150 → 1

Compiler

Compiled 20714 to 14001 computations (32.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	19
2	38	19
3	48	19
4	59	19
5	75	19
6	81	19
7	82	19
8	78	19

end1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample870.0ms (14.2%)

Algorithm

1×

intervals

Results

440.0ms	7999×	body	128	valid
34.0ms	500×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 128 to 87 computations (32% saved)

Details

analyze1.6s (25.7%)

sample76.0ms (1.2%)

simplify98.0ms (1.6%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series95.0ms (1.5%)

rewrite12.0ms (0.2%)

simplify138.0ms (2.2%)

prune153.0ms (2.5%)

localize9.0ms (0.1%)

series68.0ms (1.1%)

rewrite46.0ms (0.7%)

simplify196.0ms (3.2%)

prune266.0ms (4.3%)

localize12.0ms (0.2%)

series93.0ms (1.5%)

rewrite39.0ms (0.6%)

simplify157.0ms (2.6%)

prune178.0ms (2.9%)

localize10.0ms (0.2%)

series117.0ms (1.9%)

rewrite48.0ms (0.8%)

simplify496.0ms (8.1%)

prune242.0ms (3.9%)

regimes1.1s (18.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample870.0ms (14.2%)

Profiling