Details

analyze614.0ms (11.5%)

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
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
41.7%	58.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.0s (19.5%)

Symmetry

(sort y t)

Results

901.0ms	8256×	body	128	valid
50.0ms	397×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
750×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
204×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	88	13
4	231	13
5	568	13
6	1029	13
7	1474	13
8	1787	13
9	1744	13
10	1744	13
11	1905	13
12	1905	13
13	1862	13

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

6.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	6.3b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 t z))
✓	6.3b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series99.0ms (1.9%)

Counts

2 → 84

Calls

2 calls:

90.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
9.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

13.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
8.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

simplify117.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
452×	`associate-/l*_binary64`
442×	`associate-/r*_binary64`
280×	`associate-l_binary64`
188×	`fma-def_binary64`

Counts

173 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	5441
1	1244	5124
2	4955	5124
3	5000	5124

prune160.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	187	6	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	6	194

Error

0.0b

Counts

194 → 6

Alt Table

Status	Error	Program
	20.6b	(/.f64 x (/.f64 (.f64 (-.f64 y z) (-.f64 (.f64 t t) (*.f64 z z))) (+.f64 t z)))
	44.6b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 (.f64 t t) (.f64 z z)))) (*.f64 (+.f64 y z) (+.f64 t z)))
	10.9b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
▶	1.8b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	2.4b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	4.4b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y z) (/.f64 (cbrt.f64 x) (-.f64 t z))))

Compiler

Compiled 5714 to 2103 computations (63.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series105.0ms (2%)

Counts

3 → 96

Calls

3 calls:

84.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
14.0ms	(/.f64 x (-.f64 t z))
6.0ms	(/.f64 1 (-.f64 y z))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
67×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 156

Calls

3 calls:

15.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
4.0ms	(/.f64 1 (-.f64 y z))
3.0ms	(/.f64 x (-.f64 t z))

simplify116.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

719×	`times-frac_binary64`
570×	`associate-/l*_binary64`
453×	`associate-/r*_binary64`
186×	`associate-*l/_binary64`
181×	`associate-*r/_binary64`

Counts

252 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	457	6865
1	1402	6443
2	5057	6443

prune203.0ms (3.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	276	2	278
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	279	5	284

Error

0.0b

Counts

284 → 5

Alt Table

Status	Error	Program
	2.4b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	44.6b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 (.f64 t t) (.f64 z z)))) (*.f64 (+.f64 y z) (+.f64 t z)))
	10.9b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
	2.4b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
▶	1.8b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 1 (/.f64 (-.f64 t z) x)))

Compiler

Compiled 7404 to 2902 computations (60.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (-.f64 y z))
✓	0.0b	(/.f64 (-.f64 t z) x)
✓	0.9b	(/.f64 1 (/.f64 (-.f64 t z) x))
✓	1.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 1 (/.f64 (-.f64 t z) x)))

series106.0ms (2%)

Counts

3 → 112

Calls

3 calls:

84.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 1 (/.f64 (-.f64 t z) x)))
14.0ms	(/.f64 1 (/.f64 (-.f64 t z) x))
8.0ms	(/.f64 (-.f64 t z) x)

rewrite73.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

277×	`times-frac_binary64`
228×	`add-sqr-sqrt_binary64`
192×	`*-un-lft-identity_binary64`
125×	`add-cube-cbrt_binary64`
99×	`add-exp-log_binary64`

Counts

3 → 291

Calls

3 calls:

28.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 1 (/.f64 (-.f64 t z) x)))
7.0ms	(/.f64 1 (/.f64 (-.f64 t z) x))
4.0ms	(/.f64 (-.f64 t z) x)

simplify261.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

624×	`times-frac_binary64`
552×	`associate-/l*_binary64`
433×	`associate-/r*_binary64`
211×	`associate-/r/_binary64`
205×	`associate-*l/_binary64`

Counts

403 → 456

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	486	9827
1	1471	8791
2	4897	8788
3	4976	8788

prune339.0ms (6.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	510	2	512
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	512	5	517

Error

Counts

517 → 5

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 1 (/.f64 (-.f64 t z) x)))
▶	2.3b	(pow.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t z) x)) -1)
	6.3b	(.f64 (.f64 (/.f64 1 (-.f64 y z)) (/.f64 1 (-.f64 t z))) x)
	10.9b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
	2.4b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 13242 to 5314 computations (59.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t z) x)
✓	0.9b	(pow.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t z) x)) -1)
✓	1.5b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t z) x))

series125.0ms (2.3%)

Counts

2 → 96

Calls

2 calls:

98.0ms	(pow.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t z) x)) -1)
27.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t z) x))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
19×	`associate-r_binary64`
16×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 67

Calls

2 calls:

15.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t z) x))
7.0ms	(pow.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t z) x)) -1)

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

754×	`times-frac_binary64`
614×	`associate-/l*_binary64`
511×	`associate-/r*_binary64`
214×	`fma-def_binary64`
123×	`*-commutative_binary64`

Counts

163 → 175

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	448	6245
1	1480	5951
2	4998	5951

prune169.0ms (3.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	226	5	231

Error

Counts

231 → 5

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 1 (/.f64 (-.f64 t z) x)))
✓	2.3b	(pow.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t z) x)) -1)
	6.3b	(.f64 (.f64 (/.f64 1 (-.f64 y z)) (/.f64 1 (-.f64 t z))) x)
	10.9b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
	2.4b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 6757 to 2706 computations (60% saved)

regimes1.3s (23.9%)

Accuracy

Total 0.7b remaining (97.5%)

Threshold costs 0.7b (97.5%)

Counts

170 → 3

Compiler

Compiled 19561 to 12199 computations (37.6% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	79
1	41	79
2	52	79
3	62	79
4	72	79
5	77	79
6	79	79
7	78	79

end222.0ms (4.2%)

Compiler: Compiled 312 to 152 computations (51.3% saved)

Details

analyze614.0ms (11.5%)

sample1.0s (19.5%)

simplify75.0ms (1.4%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series99.0ms (1.9%)

rewrite28.0ms (0.5%)

simplify117.0ms (2.2%)

prune160.0ms (3%)

localize7.0ms (0.1%)

series105.0ms (2%)

rewrite33.0ms (0.6%)

simplify116.0ms (2.2%)

prune203.0ms (3.8%)

localize9.0ms (0.2%)

series106.0ms (2%)

rewrite73.0ms (1.4%)

simplify261.0ms (4.9%)

prune339.0ms (6.4%)

localize9.0ms (0.2%)

series125.0ms (2.3%)

rewrite27.0ms (0.5%)

simplify95.0ms (1.8%)

prune169.0ms (3.2%)

regimes1.3s (23.9%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

end222.0ms (4.2%)

Profiling