Details

analyze1.4s (11.4%)

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 (9.3%)

Results

1.0s	8251×	body	128	valid
68.0ms	513×	body	128	invalid
1.0ms	4×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify99.0ms (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

2.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	2.6b	(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))
✓	2.6b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series81.0ms (0.7%)

Counts

2 → 96

Calls

2 calls:

53.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
28.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))

rewrite8.0ms (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:

5.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
0.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

simplify125.0ms (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

prune126.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	143	5	148

Error

Counts

148 → 5

Alt Table

Status	Error	Program
	35.0b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
✓	2.6b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
▶	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	15.9b	(fma.f64 (cbrt.f64 (pow.f64 (/.f64 a (-.f64 (+.f64 1 t) z)) 3)) (-.f64 z y) x)
	12.6b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 4622 to 2253 computations (51.3% saved)

localize9.0ms (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)
✓	10.0b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series126.0ms (1%)

Counts

3 → 144

Calls

3 calls:

61.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
54.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
10.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite182.0ms (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:

35.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
11.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
6.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify1.1s (8.6%)

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

prune598.0ms (4.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	668	2	670
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	670	5	675

Error

Counts

675 → 5

Alt Table

Status	Error	Program
	35.0b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
✓	2.6b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	12.6b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
▶	0.1b	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (/.f64 1 a)))

Compiler

Compiled 34674 to 14892 computations (57.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series149.0ms (1.2%)

Counts

3 → 144

Calls

3 calls:

65.0ms	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (/.f64 1 a)))
51.0ms	(/.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (/.f64 1 a))
33.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

rewrite820.0ms (6.6%)

Algorithm

1×	rewrite-expression-head

Rules

5107×	`times-frac_binary64`
4602×	`*-un-lft-identity_binary64`
2943×	`add-sqr-sqrt_binary64`
2246×	`add-cube-cbrt_binary64`
1224×	`prod-diff_binary64`

Counts

3 → 2185

Calls

3 calls:

112.0ms	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (/.f64 1 a)))
19.0ms	(/.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (/.f64 1 a))
8.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

simplify2.9s (23.5%)

Algorithm

1×	egg-herbie

Rules

356×	`fma-udef_binary64`
275×	`fma-def_binary64`
265×	`neg-mul-1_binary64`
262×	`neg-sub0_binary64`
203×	`associate-*r/_binary64`

Counts

2329 → 1703

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1644	209018
1	4942	208704
2	5169	208704

prune2.4s (19.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1703	0	1703
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1703	5	1708

Error

Counts

1708 → 5

Alt Table

Status	Error	Program
	35.0b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
✓	2.6b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	12.6b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	0.1b	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (/.f64 1 a)))

Compiler

Compiled 125907 to 62610 computations (50.3% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	0.0b	(*.f64 a (-.f64 y z))
✓	11.9b	(/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z))

series126.0ms (1%)

Counts

3 → 120

Calls

3 calls:

66.0ms	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
52.0ms	(/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z))
8.0ms	(*.f64 a (-.f64 y z))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
54×	`prod-diff_binary64`
42×	`add-cube-cbrt_binary64`
30×	`times-frac_binary64`

Counts

3 → 149

Calls

3 calls:

9.0ms	(/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z))
9.0ms	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
7.0ms	(*.f64 a (-.f64 y z))

simplify191.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

535×	`times-frac_binary64`
516×	`associate-/l*_binary64`
255×	`associate-/r*_binary64`
178×	`sub-neg_binary64`
166×	`+-commutative_binary64`

Counts

269 → 271

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	613	10658
1	1695	9139
2	4931	9139
3	5005	9139

prune257.0ms (2.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	271	5	276

Error

Counts

276 → 5

Alt Table

Status	Error	Program
✓	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	0.1b	(-.f64 x (/.f64 a (/.f64 (-.f64 (+.f64 1 t) z) (-.f64 y z))))
✓	12.6b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	0.1b	(-.f64 x (/.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (/.f64 1 a)))
✓	2.6b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 10899 to 5150 computations (52.7% saved)

regimes442.0ms (3.5%)

Accuracy

Total 0.2b remaining (96.8%)

Threshold costs 0.2b (96.8%)

Counts

65 → 1

Compiler

Compiled 8283 to 5595 computations (32.5% saved)

simplify4.0ms (0%)

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

end70.0ms (0.6%)

Compiler: Compiled 127 to 85 computations (33.1% saved)

Details

analyze1.4s (11.4%)

sample1.2s (9.3%)

simplify99.0ms (0.8%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series81.0ms (0.7%)

rewrite8.0ms (0.1%)

simplify125.0ms (1%)

prune126.0ms (1%)

localize9.0ms (0.1%)

series126.0ms (1%)

rewrite182.0ms (1.5%)

simplify1.1s (8.6%)

prune598.0ms (4.8%)

localize10.0ms (0.1%)

series149.0ms (1.2%)

rewrite820.0ms (6.6%)

simplify2.9s (23.5%)

prune2.4s (19.2%)

localize14.0ms (0.1%)

series126.0ms (1%)

rewrite37.0ms (0.3%)

simplify191.0ms (1.5%)

prune257.0ms (2.1%)

regimes442.0ms (3.5%)

simplify4.0ms (0%)

end70.0ms (0.6%)

Profiling