Details

analyze1.2s (13.8%)

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
0%	99.8%	0.2%	5
12.5%	87.3%	0.2%	6
12.5%	87.3%	0.2%	7
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
28.1%	71.7%	0.2%	10
42.1%	57.7%	0.2%	11
42.1%	57.7%	0.2%	12
42.1%	57.7%	0.2%	13
49.1%	50.7%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.2s (13.6%)

Results

1.1s	8255×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify120.0ms (1.4%)

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

2.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.7b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	2.2b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

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))
✓	2.2b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series165.0ms (1.9%)

Counts

2 → 96

Calls

2 calls:

107.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
57.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))

rewrite29.0ms (0.3%)

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:

22.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
1.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

simplify244.0ms (2.9%)

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

prune261.0ms (3.1%)

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
▶	2.7b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	30.8b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	10.7b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	2.2b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 4582 to 2225 computations (51.4% saved)

localize19.0ms (0.2%)

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)
✓	9.5b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series280.0ms (3.3%)

Counts

3 → 144

Calls

3 calls:

144.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
112.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
23.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite286.0ms (3.4%)

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:

44.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
29.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
15.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify1.2s (14.4%)

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

prune774.0ms (9.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	666	4	670
Fresh	2	0	2
Picked	0	1	1
Done	1	0	1
Total	669	5	674

Error

Counts

674 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
	10.6b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	2.7b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	2.2b	(-.f64 x (.f64 (-.f64 y z) (.f64 (/.f64 1 (-.f64 (+.f64 1 t) z)) a)))
	1.1b	(-.f64 x (.f64 (/.f64 1 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a)))))

Compiler

Compiled 34707 to 14913 computations (57% saved)

localize16.0ms (0.2%)

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)) a))
✓	0.0b	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
✓	0.8b	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)

series199.0ms (2.4%)

Counts

3 → 144

Calls

3 calls:

93.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
60.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
45.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

rewrite64.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
29×	`add-cube-cbrt_binary64`

Counts

3 → 126

Calls

3 calls:

22.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
19.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
6.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

simplify220.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

516×	`times-frac_binary64`
374×	`associate-/l*_binary64`
277×	`associate-/r*_binary64`
246×	`+-commutative_binary64`
207×	`sub-neg_binary64`

Counts

270 → 292

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	658	10133
1	1956	9941
2	4965	9941
3	4992	9941

prune348.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	293	4	297

Error

Counts

297 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
	10.6b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
▶	0.7b	(-.f64 x (.f64 (.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
✓	2.7b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 10910 to 5204 computations (52.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.6b	(cbrt.f64 a)
✓	0.9b	(.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (.f64 (cbrt.f64 a) (cbrt.f64 a)))

series625.0ms (7.4%)

Counts

4 → 120

Calls

4 calls:

410.0ms	(.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (.f64 (cbrt.f64 a) (cbrt.f64 a)))
95.0ms	(.f64 (.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
62.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
57.0ms	(cbrt.f64 a)

rewrite100.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
38×	`associate-l_binary64`
36×	`add-exp-log_binary64`
26×	`times-frac_binary64`

Counts

4 → 141

Calls

4 calls:

41.0ms	(.f64 (.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
28.0ms	(.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (.f64 (cbrt.f64 a) (cbrt.f64 a)))
9.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
1.0ms	(cbrt.f64 a)

simplify253.0ms (3%)

Algorithm

1×	egg-herbie

Rules

600×	`times-frac_binary64`
530×	`fma-def_binary64`
519×	`associate-/l*_binary64`
348×	`associate-/r*_binary64`
194×	`+-commutative_binary64`

Counts

261 → 275

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	655	9316
1	2060	8092
2	5283	8092

prune305.0ms (3.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	309	4	313

Error

Counts

313 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
	10.6b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	0.7b	(-.f64 x (.f64 (.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
✓	2.7b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 12449 to 5852 computations (53% saved)

regimes516.0ms (6.1%)

Accuracy

Total 0.2b remaining (93.9%)

Threshold costs 0.2b (93.9%)

Counts

76 → 1

Compiler

Compiled 10530 to 6967 computations (33.8% 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	40	19
3	54	19
4	73	19
5	81	19
6	82	19
7	78	19

end64.0ms (0.8%)

Compiler: Compiled 115 to 75 computations (34.8% saved)

Details

analyze1.2s (13.8%)

sample1.2s (13.6%)

simplify120.0ms (1.4%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series165.0ms (1.9%)

rewrite29.0ms (0.3%)

simplify244.0ms (2.9%)

prune261.0ms (3.1%)

localize19.0ms (0.2%)

series280.0ms (3.3%)

rewrite286.0ms (3.4%)

simplify1.2s (14.4%)

prune774.0ms (9.2%)

localize16.0ms (0.2%)

series199.0ms (2.4%)

rewrite64.0ms (0.8%)

simplify220.0ms (2.6%)

prune348.0ms (4.1%)

localize14.0ms (0.2%)

series625.0ms (7.4%)

rewrite100.0ms (1.2%)

simplify253.0ms (3%)

prune305.0ms (3.6%)

regimes516.0ms (6.1%)

simplify4.0ms (0%)

end64.0ms (0.8%)

Profiling