Details

analyze1.6s (12.6%)

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
4.3%	95.5%	0.2%	11
6.4%	93.3%	0.2%	12
7.9%	91.9%	0.2%	13
13.7%	86%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.2s (9.4%)

Results

1.0s	8254×	body	128	valid
67.0ms	512×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify97.0ms (0.8%)

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%)

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

1.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.6b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	1.3b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 100 to 63 computations (37% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 (-.f64 t z) 1))
✓	1.3b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series71.0ms (0.6%)

Counts

2 → 96

Calls

2 calls:

50.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
20.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))

rewrite10.0ms (0.1%)

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:

6.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
0.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

simplify123.0ms (1%)

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

prune151.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	144	4	148

Error

0.0b

Counts

148 → 4

Alt Table

Status	Error	Program
▶	1.6b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	37.3b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	10.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	1.3b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 4582 to 2225 computations (51.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	7.2b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series118.0ms (0.9%)

Counts

3 → 144

Calls

3 calls:

58.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
47.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
12.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite191.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

1052×	`*-un-lft-identity_binary64`
883×	`times-frac_binary64`
649×	`add-sqr-sqrt_binary64`
448×	`add-cube-cbrt_binary64`
300×	`prod-diff_binary64`

Counts

3 → 600

Calls

3 calls:

37.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
10.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
8.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify911.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

435×	`times-frac_binary64`
336×	`sub-neg_binary64`
248×	`fma-def_binary64`
208×	`fma-udef_binary64`
196×	`neg-sub0_binary64`

Counts

744 → 670

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1050	52563
1	3195	48069
2	4814	47566
3	4994	47566

prune633.0ms (5.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	668	2	670
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	669	5	674

Error

Counts

674 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	32.4b	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (sqrt.f64 (/.f64 (+.f64 (-.f64 t z) 1) a))) (sqrt.f64 (/.f64 (+.f64 (-.f64 t z) 1) a))))
✓	1.6b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	1.7b	(-.f64 x (/.f64 1 (/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z))))
	10.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 34702 to 14908 computations (57% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z))))
	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	0.4b	(/.f64 1 (/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z)))
✓	7.0b	(/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z))

series142.0ms (1.1%)

Counts

3 → 156

Calls

3 calls:

60.0ms	(-.f64 x (/.f64 1 (/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z))))
44.0ms	(/.f64 1 (/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z)))
38.0ms	(/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z))

rewrite712.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Rules

4432×	`times-frac_binary64`
3880×	`*-un-lft-identity_binary64`
2607×	`add-sqr-sqrt_binary64`
1936×	`add-cube-cbrt_binary64`
924×	`prod-diff_binary64`

Counts

3 → 1830

Calls

3 calls:

102.0ms	(-.f64 x (/.f64 1 (/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z))))
22.0ms	(/.f64 1 (/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z)))
12.0ms	(/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z))

simplify2.6s (20.8%)

Algorithm

1×	egg-herbie

Rules

533×	`times-frac_binary64`
299×	`fma-def_binary64`
238×	`+-commutative_binary64`
224×	`fma-udef_binary64`
171×	`associate-+r+_binary64`

Counts

1986 → 1568

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1330	170853
1	3876	164225
2	4978	164225

prune1.9s (15.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1634	0	1634
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1634	5	1639

Error

Counts

1639 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	32.4b	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (sqrt.f64 (/.f64 (+.f64 (-.f64 t z) 1) a))) (sqrt.f64 (/.f64 (+.f64 (-.f64 t z) 1) a))))
✓	1.6b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	1.7b	(-.f64 x (/.f64 1 (/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z))))
▶	10.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 105587 to 53021 computations (49.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	5.5b	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))
✓	7.8b	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))

series159.0ms (1.3%)

Counts

4 → 135

Calls

4 calls:

70.0ms	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
33.0ms	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))
30.0ms	(+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x)
24.0ms	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))

rewrite66.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
48×	`prod-diff_binary64`
48×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`

Counts

4 → 172

Calls

4 calls:

21.0ms	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
12.0ms	(+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x)
6.0ms	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))
6.0ms	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))

simplify176.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

503×	`times-frac_binary64`
428×	`associate-/l*_binary64`
229×	`associate-/r*_binary64`
197×	`+-commutative_binary64`
193×	`sub-neg_binary64`

Counts

307 → 341

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	636	13467
1	1910	11552
2	5028	11552

prune338.0ms (2.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	341	5	346

Error

Counts

346 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	32.4b	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (sqrt.f64 (/.f64 (+.f64 (-.f64 t z) 1) a))) (sqrt.f64 (/.f64 (+.f64 (-.f64 t z) 1) a))))
✓	1.6b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	1.7b	(-.f64 x (/.f64 1 (/.f64 (/.f64 (+.f64 (-.f64 t z) 1) a) (-.f64 y z))))
✓	10.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 15535 to 7958 computations (48.8% saved)

regimes1.2s (9.9%)

Accuracy

Total 0.2b remaining (93.9%)

Threshold costs 0.2b (93.9%)

Counts

128 → 1

Compiler

Compiled 18160 to 12371 computations (31.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	29	19
2	46	19
3	64	19
4	78	19
5	82	19
6	78	19

end75.0ms (0.6%)

Compiler: Compiled 145 to 96 computations (33.8% saved)

Details

analyze1.6s (12.6%)

sample1.2s (9.4%)

simplify97.0ms (0.8%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series71.0ms (0.6%)

rewrite10.0ms (0.1%)

simplify123.0ms (1%)

prune151.0ms (1.2%)

localize8.0ms (0.1%)

series118.0ms (0.9%)

rewrite191.0ms (1.5%)

simplify911.0ms (7.3%)

prune633.0ms (5.1%)

localize10.0ms (0.1%)

series142.0ms (1.1%)

rewrite712.0ms (5.7%)

simplify2.6s (20.8%)

prune1.9s (15.2%)

localize10.0ms (0.1%)

series159.0ms (1.3%)

rewrite66.0ms (0.5%)

simplify176.0ms (1.4%)

prune338.0ms (2.7%)

regimes1.2s (9.9%)

simplify3.0ms (0%)

end75.0ms (0.6%)

Profiling